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On self-shrinkers of medium entropy inℝ4 论ℝ4 中熵的自收缩器
Geometry & Topology Pub Date : 2021-06-18 DOI: 10.2140/gt.2023.27.3715
Alexander Mramor
{"title":"On self-shrinkers of medium entropy in\u0000ℝ4","authors":"Alexander Mramor","doi":"10.2140/gt.2023.27.3715","DOIUrl":"https://doi.org/10.2140/gt.2023.27.3715","url":null,"abstract":"In this article we study smooth asymptotically conical self shrinkers in $mathbb{R}^4$ with Colding-Minicozzi entropy bounded above by $Lambda_{1}$.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"111 25","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138599733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classifying sufficiently connected PSC manifoldsin 4 and 5 dimensions 在4维和5维上对充分连接的PSC流形进行分类
Geometry & Topology Pub Date : 2021-05-15 DOI: 10.2140/gt.2023.27.1635
Otis Chodosh, Chao Li, Yevgeny Liokumovich
{"title":"Classifying sufficiently connected PSC manifolds\u0000in 4 and 5 dimensions","authors":"Otis Chodosh, Chao Li, Yevgeny Liokumovich","doi":"10.2140/gt.2023.27.1635","DOIUrl":"https://doi.org/10.2140/gt.2023.27.1635","url":null,"abstract":"We show that if $N$ is a closed manifold of dimension $n=4$ (resp. $n=5$) with $pi_2(N) = 0$ (resp. $pi_2(N)=pi_3(N)=0$) that admits a metric of positive scalar curvature, then a finite cover $hat N$ of $N$ is homotopy equivalent to $S^n$ or connected sums of $S^{n-1}times S^1$. Our approach combines recent advances in the study of positive scalar curvature with a novel argument of Alpert--Balitskiy--Guth. Additionally, we prove a more general mapping version of this result. In particular, this implies that if $N$ is a closed manifold of dimensions $4$ or $5$, and $N$ admits a map of nonzero degree to a closed aspherical manifold, then $N$ does not admit any Riemannian metric with positive scalar curvature.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128448022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
A global Weinstein splitting theorem for holomorphic Poisson manifolds 全纯泊松流形的全局Weinstein分裂定理
Geometry & Topology Pub Date : 2021-02-25 DOI: 10.2140/gt.2022.26.2831
S. Druel, J. Pereira, Brent Pym, Fr'ed'eric Touzet
{"title":"A global Weinstein splitting theorem for holomorphic Poisson manifolds","authors":"S. Druel, J. Pereira, Brent Pym, Fr'ed'eric Touzet","doi":"10.2140/gt.2022.26.2831","DOIUrl":"https://doi.org/10.2140/gt.2022.26.2831","url":null,"abstract":"We prove that if a compact K¨ahler Poisson manifold has a symplectic leaf with finite fundamental group, then after passing to a finite ´etale cover, it decomposes as the product of the universal cover of the leaf and some other Poisson manifold. As a step in the proof, we establish a special case of Beauville’s conjecture on the structure of compact K¨ahler manifolds with split tangent bundle.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121072413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Cellular objects in isotropic motivic categories 各向同性动力类别中的细胞对象
Geometry & Topology Pub Date : 2021-02-09 DOI: 10.2140/gt.2023.27.2013
Fabio Tanania
{"title":"Cellular objects in isotropic motivic categories","authors":"Fabio Tanania","doi":"10.2140/gt.2023.27.2013","DOIUrl":"https://doi.org/10.2140/gt.2023.27.2013","url":null,"abstract":"Our main purpose is to describe the category of isotropic cellular spectra over flexible fields. Guided by [6], we show that it is equivalent, as a stable $infty$-category equipped with a $t$-structure, to the derived category of left comodules over the dual of the classical topological Steenrod algebra. In order to obtain this result, the category of isotropic cellular modules over the motivic Brown-Peterson spectrum is also studied, and isotropic Adams and Adams-Novikov spectral sequences are developed. As a consequence, we also compute hom sets in the category of isotropic Tate motives between motives of isotropic cellular spectra.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130961693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Collapsing Calabi–Yau fibrations and uniformdiameter bounds 塌缩的Calabi-Yau振动和等径界
Geometry & Topology Pub Date : 2021-01-24 DOI: 10.2140/gt.2023.27.397
Yang Li
{"title":"Collapsing Calabi–Yau fibrations and uniform\u0000diameter bounds","authors":"Yang Li","doi":"10.2140/gt.2023.27.397","DOIUrl":"https://doi.org/10.2140/gt.2023.27.397","url":null,"abstract":"As a sequel to cite{Licollapsing}, we study Calabi-Yau metrics collapsing along a holomorphic fibration over a Riemann surface. Assuming at worst canonical singular fibres, we prove a uniform diameter bound for all fibres in the suitable rescaling. This has consequences on the geometry around the singular fibres.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130354629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The infimum of the dual volume of convexcocompact hyperbolic 3–manifolds 凸紧双曲3 -流形对偶体积的最小值
Geometry & Topology Pub Date : 2021-01-22 DOI: 10.2140/gt.2023.27.2319
Filippo Mazzoli
{"title":"The infimum of the dual volume of convex\u0000cocompact hyperbolic 3–manifolds","authors":"Filippo Mazzoli","doi":"10.2140/gt.2023.27.2319","DOIUrl":"https://doi.org/10.2140/gt.2023.27.2319","url":null,"abstract":"We show that the infimum of the dual volume of the convex core of a convex co-compact hyperbolic $3$-manifold with incompressible boundary coincides with the infimum of the Riemannian volume of its convex core, as we vary the geometry by quasi-isometric deformations. We deduce a linear lower bound of the volume of the convex core of a quasi-Fuchsian manifold in terms of the length of its bending measured lamination, with optimal multiplicative constant.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116631454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algebraic Spivak’s theorem andapplications 代数斯皮瓦克定理及其应用
Geometry & Topology Pub Date : 2021-01-11 DOI: 10.2140/gt.2023.27.351
Toni Annala
{"title":"Algebraic Spivak’s theorem and\u0000applications","authors":"Toni Annala","doi":"10.2140/gt.2023.27.351","DOIUrl":"https://doi.org/10.2140/gt.2023.27.351","url":null,"abstract":"We prove an analogue of Lowrey--Sch\"urg's algebraic Spivak's theorem when working over a base ring $A$ that is either a field or a nice enough discrete valuation ring, and after inverting the residual characteristic exponent $e$ in the coefficients. By this result algebraic bordism groups of quasi-projective derived $A$-schemes can be generated by classical cycles, leading to vanishing results for low degree $e$-inverted bordism classes, as well as to the classification of quasi-smooth projective $A$-schemes of low virtual dimension up to $e$-inverted cobordism. As another application, we prove that $e$-inverted bordism classes can be extended from an open subset, leading to the proof of homotopy invariance of $e$-inverted bordism groups for quasi-projective derived $A$-schemes.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122079182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Cohomological χ–independence for moduli ofone-dimensional sheaves and moduli of Higgs bundles 一维束模与希格斯束模的上同调无关性
Geometry & Topology Pub Date : 2020-12-11 DOI: 10.2140/gt.2023.27.1539
D. Maulik, Junliang Shen
{"title":"Cohomological χ–independence for moduli of\u0000one-dimensional sheaves and moduli of Higgs bundles","authors":"D. Maulik, Junliang Shen","doi":"10.2140/gt.2023.27.1539","DOIUrl":"https://doi.org/10.2140/gt.2023.27.1539","url":null,"abstract":"We prove that the intersection cohomology (together with the perverse and the Hodge filtrations) for the moduli space of one-dimensional semistable sheaves supported in an ample curve class on a toric del Pezzo surface is independent of the Euler characteristic of the sheaves. We also prove an analogous result for the moduli space of semistable Higgs bundles with respect to an effective divisor $D$ of degree $mathrm{deg}(D)>2g-2$. Our results confirm the cohomological $chi$-independence conjecture by Bousseau for $mathbb{P}^2$, and verify Toda's conjecture for Gopakumar-Vafa invariants for certain local curves and local surfaces. \u0000For the proof, we combine a generalized version of Ngo's support theorem, a dimension estimate for the stacky Hilbert-Chow morphism, and a splitting theorem for the morphism from the moduli stack to the good GIT quotient.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117105742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 30
Equations of linear subvarieties of strata of differentials 微分层的线性亚变量方程
Geometry & Topology Pub Date : 2020-11-23 DOI: 10.2140/gt.2022.26.2773
Frederik Benirschke, B. Dozier, S. Grushevsky
{"title":"Equations of linear subvarieties of strata of differentials","authors":"Frederik Benirschke, B. Dozier, S. Grushevsky","doi":"10.2140/gt.2022.26.2773","DOIUrl":"https://doi.org/10.2140/gt.2022.26.2773","url":null,"abstract":"For a linear subvariety $M$ of a stratum of meromorphic differentials, we investigate its closure in the multi-scale compactification constructed by Bainbridge-Chen-Gendron-Grushevsky-Moller. We prove various restrictions on the type of defining linear equations in period coordinates for $M$ near its boundary, and prove that the closure is locally a toric variety. As applications, we give a fundamentally new proof of a generalization of the cylinder deformation theorem of Wright to the case of meromorphic strata, and construct a smooth compactification of the Hurwitz space of covers of the Riemann sphere.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"61 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120987026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Linear independence of rationally slice knots 合理切片节的线性独立性
Geometry & Topology Pub Date : 2020-11-15 DOI: 10.2140/gt.2022.26.3143
Jennifer Hom, Sungkyung Kang, Junghwan Park, Matthew Stoffregen
{"title":"Linear independence of rationally slice knots","authors":"Jennifer Hom, Sungkyung Kang, Junghwan Park, Matthew Stoffregen","doi":"10.2140/gt.2022.26.3143","DOIUrl":"https://doi.org/10.2140/gt.2022.26.3143","url":null,"abstract":"A knot in $S^3$ is rationally slice if it bounds a disk in a rational homology ball. We give an infinite family of rationally slice knots that are linearly independent in the knot concordance group. In particular, our examples are all infinite order. All previously known examples of rationally slice knots were order two.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127715397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
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