Geometric and Functional Analysis最新文献

{"title":"Circle Bundles with PSC over Large Manifolds","authors":"Aditya Kumar, Balarka Sen","doi":"10.1007/s00039-025-00723-z","DOIUrl":"https://doi.org/10.1007/s00039-025-00723-z","url":null,"abstract":"We construct infinitely many examples of macroscopically large manifolds of dimension <jats:inline-formula> <jats:alternatives> <jats:tex-math>$m geq 4$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>m</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>4</mml:mn> </mml:math> </jats:alternatives> </jats:inline-formula> equipped with circle bundles whose total spaces admit metrics of positive scalar curvature and have macroscopic dimension at most <jats:inline-formula> <jats:alternatives> <jats:tex-math>$lceil m/2 rceil + 1$</jats:tex-math> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>⌈</mml:mo> <mml:mi>m</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> <mml:mo>⌉</mml:mo> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:math> </jats:alternatives> </jats:inline-formula> . In particular, we answer a question of Gromov on the existence of circle bundles over enlargeable manifolds whose total spaces admit metrics of positive scalar curvature, in all dimensions. Our constructions are based on techniques from symplectic geometry.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"7 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145404392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mixing for Dynamical Systems Driven by Stationary Noises","authors":"Sergei Kuksin, Armen Shirikyan","doi":"10.1007/s00039-025-00722-0","DOIUrl":"https://doi.org/10.1007/s00039-025-00722-0","url":null,"abstract":"The paper deals with the problem of long-time asymptotic behaviour of solutions for classes of ODEs and PDEs, perturbed by stationary noises. The latter are not assumed to be <inline-formula><alternatives><mml:math><mml:mi>δ</mml:mi></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$delta $end{document}</tex-math><inline-graphic mime-subtype=\"GIF\" specific-use=\"web\" xlink:href=\"39_2025_722_Article_IEq1.gif\"></inline-graphic></alternatives></inline-formula>-correlated in time, therefore the evolution in question is not necessarily Markovian. We first prove an abstract result which implies the mixing for random dynamical systems satisfying appropriate dissipativity and controllability conditions. It is applicable to a large class of evolution equations, and we illustrate this on the examples of a chain of anharmonic oscillators coupled to heat reservoirs, the 2d Navier–Stokes system, and a complex Ginzburg–Landau equation. Our results also apply to the general theory of random processes on the 1d lattice and allow one to get for them results related to Dobrushin’s theorems on reconstructing processes via their conditional distributions. The proof is based on an iterative construction with Newton’s quadratic approximation. It uses the method of Kantorovich functional, introduced earlier by the authors in the context of randomly forced PDEs, and some ideas used by them in the Markovian case to prove mixing with the help of controllability properties of an associated system.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"186 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145914890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spherical Caps do Not Always Maximize Neumann Eigenvalues on the Sphere","authors":"Dorin Bucur, Richard S. Laugesen, Eloi Martinet, Mickaël Nahon","doi":"10.1007/s00039-025-00721-1","DOIUrl":"https://doi.org/10.1007/s00039-025-00721-1","url":null,"abstract":"We prove the existence of an open set <inline-formula><alternatives><mml:math><mml:mi mathvariant=\"normal\">Ω</mml:mi><mml:mo>⊂</mml:mo><mml:msup><mml:mi mathvariant=\"double-struck\">S</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math><tex-math>documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$Omega subset mathbb{S}^{2}$end{document}</tex-math><inline-graphic mime-subtype=\"GIF\" specific-use=\"web\" xlink:href=\"39_2025_721_Article_IEq1.gif\"></inline-graphic></alternatives></inline-formula> for which the first positive eigenvalue of the Laplacian with Neumann boundary condition exceeds that of the geodesic disk having the same area. This example holds for large areas and contrasts with results by Bandle and later authors proving the maximality of the disk under additional topological or geometric conditions, thereby revealing such conditions to be necessary.","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"43 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145914889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Affirmative Resolution of Bourgain’s Slicing Problem Using Guan’s Bound","authors":"Boaz Klartag, Joseph Lehec","doi":"10.1007/s00039-025-00718-w","DOIUrl":"https://doi.org/10.1007/s00039-025-00718-w","url":null,"abstract":"<p>We provide the final step in the resolution of Bourgain’s slicing problem in the affirmative. Thus we establish the following theorem: for any convex body <span><span style=\"\">K subseteq mathbb{R}^{n}</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.313ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -778.3 3470.7 995.9\" width=\"8.061ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-4B\" y=\"0\"></use><use x=\"1167\" xlink:href=\"#MJMAIN-2286\" y=\"0\"></use><g transform=\"translate(2223,0)\"><use x=\"0\" xlink:href=\"#MJAMS-52\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1021\" xlink:href=\"#MJMATHI-6E\" y=\"581\"></use></g></g></svg></span><script type=\"math/tex\">K subseteq mathbb{R}^{n}</script></span> of volume one, there exists a hyperplane <span><span style=\"\">H subseteq mathbb{R}^{n}</span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.309ex\" role=\"img\" style=\"vertical-align: -0.505ex;\" viewbox=\"0 -777 3469.7 994.3\" width=\"8.059ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-48\" y=\"0\"></use><use x=\"1166\" xlink:href=\"#MJMAIN-2286\" y=\"0\"></use><g transform=\"translate(2222,0)\"><use x=\"0\" xlink:href=\"#MJAMS-52\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1021\" xlink:href=\"#MJMATHI-6E\" y=\"581\"></use></g></g></svg></span><script type=\"math/tex\">H subseteq mathbb{R}^{n}</script></span> such that </p><span><span style=\"\"> Vol_{n-1}(K cap H) &gt; c, </span><span style=\"font-size: 100%; display: inline-block;\" tabindex=\"0\"><svg focusable=\"false\" height=\"2.614ex\" role=\"img\" style=\"vertical-align: -0.706ex;\" viewbox=\"0 -821.4 8697.5 1125.3\" width=\"20.201ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use x=\"0\" xlink:href=\"#MJMATHI-56\" y=\"0\"></use><use x=\"769\" xlink:href=\"#MJMATHI-6F\" y=\"0\"></use><g transform=\"translate(1255,0)\"><use x=\"0\" xlink:href=\"#MJMATHI-6C\" y=\"0\"></use><g transform=\"translate(298,-150)\"><use transform=\"scale(0.707)\" x=\"0\" xlink:href=\"#MJMATHI-6E\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"600\" xlink:href=\"#MJMAIN-2212\" y=\"0\"></use><use transform=\"scale(0.707)\" x=\"1379\" xlink:href=\"#MJMAIN-31\" y=\"0\"></use></g></g><use x=\"2982\" xlink:href=\"#MJMAIN-28\" y=\"0\"></use><use x=\"3372\" xlink:href=\"#MJMATHI-4B\" y=\"0\"></use><use x=\"4483\" xlink:href=\"#MJMAIN-2229\" y=\"0\"></use><use x=\"5373\" xlink:href=\"#MJMATHI-48\" y=\"0\"></use><use x=\"6261\" xlink:href=\"#MJMAIN-29\" y=\"0\"></use><use x=\"6929\" xlink:href=\"#MJMAIN-3E\" y=\"0\"></use><use x=\"7985\" xlink:href=\"#MJMATHI-63\" y=\"0\"></use><use x=\"8419\" xlink:href=\"#MJMAIN-2C\" y=\"0\"></use></g></svg></span><script type=\"math/tex; mode=display\"> Vol_{n-1}(K cap H) >","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"28 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Semiclassical Measures for Complex Hyperbolic Quotients","authors":"Jayadev Athreya, Semyon Dyatlov, Nicholas Miller","doi":"10.1007/s00039-025-00717-x","DOIUrl":"https://doi.org/10.1007/s00039-025-00717-x","url":null,"abstract":"<p>We study semiclassical measures for Laplacian eigenfunctions on compact complex hyperbolic quotients. Geodesic flows on these quotients are a model case of hyperbolic dynamical systems with different expansion/contraction rates in different directions. We show that the support of any semiclassical measure is either equal to the entire cosphere bundle or contains the cosphere bundle of a compact immersed totally geodesic complex submanifold.</p><p>The proof uses the one-dimensional fractal uncertainty principle of Bourgain–Dyatlov (Ann. Math. (2) 187(3):825–867, 2018) along the fast expanding/contracting directions, in a way similar to the work of Dyatlov–Jézéquel (Ann. Henri Poincaré, 2023) in the toy model of quantum cat maps, together with a description of the closures of fast unstable/stable trajectories relying on Ratner theory.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"27 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"CG10543 Protein Is Involved in the Regulation of Transcription of Ecdysone-Dependent Genes","authors":"N. E. Vorobyova, Iu. V. Nikolenko, A. N. Krasnov","doi":"10.1134/s0026893325700220","DOIUrl":"https://doi.org/10.1134/s0026893325700220","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Despite increasing data on the properties of the origins of replication, the molecular mechanisms underlying the origin recognition complex (ORC) positioning in the genome are still poorly understood. It has been suggested that the key factors determining the positioning of ORC in the genome are DNA-binding proteins that form various DNA regulatory elements, including insulators, promoters, and enhancers, thereby linking the replication program to different levels of transcriptional regulation. Previously, we demonstrated that the Su(Hw) protein is the first example of such a protein. Subsequent studies identified a number of other DNA-binding proteins, including CG10543, which may be responsible for the formation of the corresponding regulatory elements and the recruitment of transcriptional and replication complexes to their binding sites. It has been shown that the Drosophila CG10543 protein interacts with the deubiquitinating (DUB) module of the SAGA complex. The binding sites of the CG10543 protein are predominantly located in the promoter regions of active genes and colocalize with the SAGA and dSWI/SNF chromatin modification and remodeling complexes, as well as with the ORC replication complex. To investigate the role of the CG10543 protein in transcriptional regulation, an RNA-Seq experiment was conducted in Drosophila S2 cells under normal conditions and upon RNA interference with the CG10543 protein. It was shown that the CG10543 protein affects the transcription of 469 genes, with a significant portion of these genes (23%) being ecdysone-dependent genes. Ecdysone is the main steroid hormone in Drosophila, is responsible for Drosophila metamorphosis, and has a significant effect on the expression of many genes during development. We demonstrated that CG10543 sites colocalize with the CBP protein and the histone mark H3K27Ac, which are characteristic of active regulatory elements. The CG10543 protein also colocalizes with the CP190 protein, suggesting a potential mechanism of transcriptional regulation through the formation of long-range interactions between regulatory elements.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"30 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local Integral Transforms and Global Spectral Decomposition","authors":"Valentin Blomer, Subhajit Jana, Paul D. Nelson","doi":"10.1007/s00039-025-00714-0","DOIUrl":"https://doi.org/10.1007/s00039-025-00714-0","url":null,"abstract":"<p>We establish an explicit global spectral decomposition of shifted convolution sums and the second moment of automorphic <span>(L)</span>-functions for Maaß forms with explicit integral transforms as well as explicit inversion formulae over every local field.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"52 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-vanishing of Geodesic Periods of Automorphic Forms","authors":"Petru Constantinescu, Asbjørn Christian Nordentoft","doi":"10.1007/s00039-025-00715-z","DOIUrl":"https://doi.org/10.1007/s00039-025-00715-z","url":null,"abstract":"<p>We prove that one hundred percent of the closed geodesic periods of a Hecke–Maaß cusp form for the modular group are non-vanishing when ordered by length. We present applications to the non-vanishing of central values of Rankin–Selberg <span>(L)</span>-functions. Similar results for holomorphic forms for general Fuchsian groups of finite covolume with a cusp are also obtained, as well as results towards normal distribution. Our new key ingredient is to relate the distributions of closed geodesic periods and vertical line integrals via graph theory.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"38 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prime Number Theorems for Polynomials from Homogeneous Dynamics","authors":"Giorgos Kotsovolis, Katharine Woo","doi":"10.1007/s00039-025-00716-y","DOIUrl":"https://doi.org/10.1007/s00039-025-00716-y","url":null,"abstract":"&lt;p&gt;We establish a new class of examples of the multivariate Bateman-Horn conjecture by using tools from dynamics. These cases include the determinant polynomial on the space of &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"1.509ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -561.7 2423.9 649.8\" width=\"5.63ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-6E\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"822\" xlink:href=\"#MJMAIN-D7\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1823\" xlink:href=\"#MJMATHI-6E\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;ntimes n&lt;/script&gt;&lt;/span&gt; matrices, the Pfaffian on the space of skew-symmetric &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"1.909ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -733.9 3424.9 822.1\" width=\"7.955ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMAIN-32\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"500\" xlink:href=\"#MJMATHI-6E\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1323\" xlink:href=\"#MJMAIN-D7\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"2323\" xlink:href=\"#MJMAIN-32\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"2824\" xlink:href=\"#MJMATHI-6E\" y=\"0\"&gt;&lt;/use&gt;&lt;/g&gt;&lt;/svg&gt;&lt;span role=\"presentation\"&gt;&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;script type=\"math/tex\"&gt;2ntimes 2n&lt;/script&gt;&lt;/span&gt; matrices, and the determinant polynomial on the space of symmetric &lt;span&gt;&lt;span style=\"\"&gt;&lt;/span&gt;&lt;span data-mathml='&lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\"&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&amp;#x00D7;&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;' role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\" tabindex=\"0\"&gt;&lt;svg aria-hidden=\"true\" focusable=\"false\" height=\"1.512ex\" role=\"img\" style=\"vertical-align: -0.205ex;\" viewbox=\"0 -562.7 2423.9 650.9\" width=\"5.63ex\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"&gt;&lt;g fill=\"currentColor\" stroke=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"&gt;&lt;use x=\"0\" xlink:href=\"#MJMATHI-6E\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"822\" xlink:href=\"#MJMAIN-D7\" y=\"0\"&gt;&lt;/use&gt;&lt;use x=\"1823\" xlink:","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"31 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Homomorphisms to 3–Manifold Groups","authors":"Daniel Groves, Michael Hull, Hao Liang","doi":"10.1007/s00039-025-00713-1","DOIUrl":"https://doi.org/10.1007/s00039-025-00713-1","url":null,"abstract":"<p>We prove foundational results about the set of homomorphisms from a finitely generated group to the collection of all fundamental groups of compact 3–manifolds and answer questions of Agol–Liu (J. Am. Math. Soc. 25(1):151–187, 2012) and Reid–Wang–Zhou (Acta Math. Sin. Engl. Ser. 18(1):157–172, 2002).</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"25 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144924672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}