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Coalgebraic formal curve spectra and spectral jet spaces 共代数形式曲线谱与谱喷空间
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-04-24 DOI: 10.2140/gt.2020.24.1
E. Peterson
{"title":"Coalgebraic formal curve spectra and spectral jet spaces","authors":"E. Peterson","doi":"10.2140/gt.2020.24.1","DOIUrl":"https://doi.org/10.2140/gt.2020.24.1","url":null,"abstract":"We import into homotopy theory the algebro-geometric construction of the cotangent space of a geometric point on a scheme. Specializing to the category of spectra local to a Morava $K$-theory of height $d$, we show that this can be used to produce a choice-free model of the determinantal sphere as well as an efficient Picard-graded cellular decomposition of $K(mathbb Z_p, d+1)$. Coupling these ideas to work of Westerland, we give a \"Snaith's theorem\" for the Iwasawa extension of the $K(d)$-local sphere.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"3 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82395175","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}
引用次数: 4
Floer homology, group orderability, and tautfoliations of hyperbolic 3–manifolds 双曲3 -流形的花同源性、群有序性和重叶化
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-04-09 DOI: 10.2140/gt.2020.24.2075
N. Dunfield
{"title":"Floer homology, group orderability, and taut\u0000foliations of hyperbolic 3–manifolds","authors":"N. Dunfield","doi":"10.2140/gt.2020.24.2075","DOIUrl":"https://doi.org/10.2140/gt.2020.24.2075","url":null,"abstract":"This paper explores the conjecture that the following are equivalent for rational homology 3-spheres: having left-orderable fundamental group, having non-minimal Heegaard Floer homology, and admitting a co-orientable taut foliation. In particular, it adds further evidence in favor of this conjecture by studying these three properties for more than 300,000 hyperbolic rational homology 3-spheres. New or much improved methods for studying each of these properties form the bulk of the paper, including a new combinatorial criterion, called a foliar orientation, for showing that a 3-manifold has a taut foliation.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"12 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76179233","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}
引用次数: 16
Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics 曲线和曲面的格式:虚类，积分，欧拉特性
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-03-21 DOI: 10.2140/gt.2021.25.3425
D. Oprea, R. Pandharipande
{"title":"Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics","authors":"D. Oprea, R. Pandharipande","doi":"10.2140/gt.2021.25.3425","DOIUrl":"https://doi.org/10.2140/gt.2021.25.3425","url":null,"abstract":"We compute tautological integrals over Quot schemes on curves and surfaces. After obtaining several explicit formulas over Quot schemes of dimension 0 quotients on curves (and finding a new symmetry), we apply the results to tautological integrals against the virtual fundamental classes of Quot schemes of dimension 0 and 1 quotients on surfaces (using also universality, torus localization, and cosection localization). The virtual Euler characteristics of Quot schemes of surfaces, a new theory parallel to the Vafa-Witten Euler characteristics of the moduli of bundles, is defined and studied. Complete formulas for the virtual Euler characteristics are found in the case of dimension 0 quotients on surfaces. Dimension 1 quotients are studied on K3 surfaces and surfaces of general type with connections to the Kawai-Yoshioka formula and the Seiberg-Witten invariants respectively. The dimension 1 theory is completely solved for minimal surfaces of general type admitting a nonsingular canonical curve. Along the way, we find a new connection between weighted tree counting and multivariate Fuss-Catalan numbers which is of independent interest.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"65 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83319995","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}
引用次数: 33
The induced metric on the boundary of the convex hull of a quasicircle in hyperbolic and anti-de Sitter geometry 双曲和反德西特几何中拟圆凸壳边界上的诱导度规
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-02-11 DOI: 10.2140/gt.2021.25.2827
F. Bonsante, J. Danciger, Sara Maloni, Jean-Marc Schlenker
{"title":"The induced metric on the boundary of the convex hull of a quasicircle in hyperbolic and anti-de Sitter geometry","authors":"F. Bonsante, J. Danciger, Sara Maloni, Jean-Marc Schlenker","doi":"10.2140/gt.2021.25.2827","DOIUrl":"https://doi.org/10.2140/gt.2021.25.2827","url":null,"abstract":"Celebrated work of Alexandrov and Pogorelov determines exactly which metrics on the sphere are induced on the boundary of a compact convex subset of hyperbolic three-space. As a step toward a generalization for unbounded convex subsets, we consider convex regions of hyperbolic three-space bounded by two properly embedded disks which meet at infinity along a Jordan curve in the ideal boundary. In this setting, it is natural to augment the notion of induced metric on the boundary of the convex set to include a gluing map at infinity which records how the asymptotic geometry of the two surfaces compares near points of the limiting Jordan curve. Restricting further to the case in which the induced metrics on the two bounding surfaces have constant curvature $K in [-1,0)$ and the Jordan curve at infinity is a quasicircle, the gluing map is naturally a quasisymmetric homeomorphism of the circle. The main result is that for each value of $K$, every quasisymmetric map is achieved as the gluing map at infinity along some quasicircle. We also prove analogous results in the setting of three-dimensional anti de Sitter geometry. Our results may be viewed as universal versions of the conjectures of Thurston and Mess about prescribing the induced metric on the boundary of the convex core of quasifuchsian hyperbolic manifolds and globally hyperbolic anti de Sitter spacetimes.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"88 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86962064","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}
引用次数: 9
More concordance homomorphisms from knot Floer homology 结花同态的更多一致性同态
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-02-09 DOI: 10.2140/gt.2021.25.275
Irving Dai, Jennifer Hom, Matthew Stoffregen, L. Truong
{"title":"More concordance homomorphisms from knot Floer homology","authors":"Irving Dai, Jennifer Hom, Matthew Stoffregen, L. Truong","doi":"10.2140/gt.2021.25.275","DOIUrl":"https://doi.org/10.2140/gt.2021.25.275","url":null,"abstract":"We define an infinite family of linearly independent, integer-valued smooth concordance homomorphisms. Our homomorphisms are explicitly computable and rely on local equivalence classes of knot Floer complexes over the ring $mathbb{F}[U, V]/(UV=0)$. We compare our invariants to other concordance homomorphisms coming from knot Floer homology, and discuss applications to topologically slice knots, concordance genus, and concordance unknotting number.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"184 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73001315","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}
引用次数: 41
Classification of tight contact structures on surgeries on the figure-eight knot 八字结手术中紧密接触结构的分类
IF 2 1区 数学
Geometry & Topology Pub Date : 2019-01-18 DOI: 10.2140/GT.2020.24.1457
J. Conway, Hyunki Min
{"title":"Classification of tight contact structures on surgeries on the figure-eight knot","authors":"J. Conway, Hyunki Min","doi":"10.2140/GT.2020.24.1457","DOIUrl":"https://doi.org/10.2140/GT.2020.24.1457","url":null,"abstract":"Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, can we classify such structures. We present the first such classification on an infinite family of (mostly) hyperbolic 3-manifolds: surgeries on the figure-eight knot. We also determine which of the tight contact structures are symplectically fillable and which are universally tight.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"36 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2019-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82237159","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}
引用次数: 8
Extending fibrations of knot complements to ribbon disk complements 将结补体的纤维延伸到带盘补体
IF 2 1区 数学
Geometry & Topology Pub Date : 2018-11-23 DOI: 10.2140/gt.2021.25.1479
Maggie Miller
{"title":"Extending fibrations of knot complements to ribbon disk complements","authors":"Maggie Miller","doi":"10.2140/gt.2021.25.1479","DOIUrl":"https://doi.org/10.2140/gt.2021.25.1479","url":null,"abstract":"We show that if $K$ is a fibered ribbon knot in $S^3=partial B^4$ bounding ribbon disk $D$, then with a transversality condition the fibration on $S^3setminusnu(K)$ extends to a fibration of $B^4setminusnu(D)$. This partially answers a question of Casson and Gordon. In particular, we show the fibration always extends when $D$ has exactly two local minima. More generally, we construct movies of singular fibrations on $4$-manifolds and describe a sufficient property of a movie to imply the underlying $4$-manifold is fibered over $S^1$.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"102 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2018-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75802654","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}
引用次数: 4
Towards conservativity of 𝔾m–stabilization 论几何稳定的保守性
IF 2 1区 数学
Geometry & Topology Pub Date : 2018-11-05 DOI: 10.2140/GT.2020.24.1969
Tom Bachmann, Maria Yakerson
{"title":"Towards conservativity of 𝔾m–stabilization","authors":"Tom Bachmann, Maria Yakerson","doi":"10.2140/GT.2020.24.1969","DOIUrl":"https://doi.org/10.2140/GT.2020.24.1969","url":null,"abstract":"We study the interplay of the homotopy coniveau tower, the Rost-Schmid complex of a strictly homotopy invariant sheaf, and homotopy modules. For a strictly homotopy invariant sheaf $M$, smooth $k$-scheme $X$ and $q geqslant 0$ we construct a novel cycle complex $C^*(X, M, q)$ and we prove that in favorable cases, $C^*(X, M, q)$ is equivalent to the homotopy coniveau tower $M^{(q)}(X)$. To do so we establish moving lemmas for the Rost-Schmid complex. As an application we deduce a cycle complex model for Milnor-Witt motivic cohomology. Furthermore we prove that if $M$ is a strictly homotopy invariant sheaf, then $M_{-2}$ is a homotopy module. Finally we conjecture that for $q>0$, $underline{pi}_0(M^{(q)})$ is a homotopy module, explain the significance of this conjecture for studying conservativity properties of the $mathbb{G}_m$-stabilization functor $mathcal{SH}^{S^1}!(k) to mathcal{SH}(k)$, and provide some evidence for the conjecture.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"38 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2018-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82365583","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}
引用次数: 7
On Kodaira fibrations with invariant cohomology 关于具有不变上同调的Kodaira颤振
IF 2 1区 数学
Geometry & Topology Pub Date : 2018-11-01 DOI: 10.2140/gt.2021.25.2385
Corey Bregman
{"title":"On Kodaira fibrations with invariant cohomology","authors":"Corey Bregman","doi":"10.2140/gt.2021.25.2385","DOIUrl":"https://doi.org/10.2140/gt.2021.25.2385","url":null,"abstract":"A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve, such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant rational cohomology in degree 1, proving that if the dimension of the holomorphic invariants is 1 or 2, then X admits a branch covering over a product of curves inducing an isomorphism on rational cohomology in degree 1. We also study the class of Kodaira fibrations possessing a holomorphic section, and demonstrate that having a section imposes no restriction on possible monodromies.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"18 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77501163","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}
引用次数: 7
Bounds on spectral norms and barcodes 谱范数和条形码的边界
IF 2 1区 数学
Geometry & Topology Pub Date : 2018-10-23 DOI: 10.2140/gt.2021.25.3257
A. Kislev, E. Shelukhin
{"title":"Bounds on spectral norms and barcodes","authors":"A. Kislev, E. Shelukhin","doi":"10.2140/gt.2021.25.3257","DOIUrl":"https://doi.org/10.2140/gt.2021.25.3257","url":null,"abstract":"We investigate the relations between algebraic structures, spectral invariants, and persistence modules, in the context of monotone Lagrangian Floer homology with Hamiltonian term. Firstly, we use the newly introduced method of filtered continuation elements to prove that the Lagrangian spectral norm controls the barcode of the Hamiltonian perturbation of the Lagrangian submanifold, up to shift, in the bottleneck distance. Moreover, we show that it satisfies Chekanov type low-energy intersection phenomena, and non-degeneracy theorems. Secondly, we introduce a new averaging method for bounding the spectral norm from above, and apply it to produce precise uniform bounds on the Lagrangian spectral norm in certain closed symplectic manifolds. Finally, by using the theory of persistence modules, we prove that our bounds are in fact sharp in some cases. Along the way we produce a new calculation of the Lagrangian quantum homology of certain Lagrangian submanifolds, and answer a question of Usher.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":"14 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2018-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75231322","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}
引用次数: 35
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