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On the topology of fillings of contact 3-manifolds 接触3流形的填充拓扑
Geometry and Topology Monographs Pub Date : 2015-12-29 DOI: 10.2140/GTM.2015.19.73
B. Ozbagci
{"title":"On the topology of fillings of contact 3-manifolds","authors":"B. Ozbagci","doi":"10.2140/GTM.2015.19.73","DOIUrl":"https://doi.org/10.2140/GTM.2015.19.73","url":null,"abstract":"Definition 1.2 An almost-complex structure on an even-dimensional manifold X is a complex structure on its tangent bundle TX , or equivalently a bundle map J W TX ! TX with J iJ D idTX . The pair .X;J / is called an almost complex manifold. It is called a complex manifold if the almost complex structure is integrable, meaning that J is induced via multiplication by i in any holomorphic coordinate chart.","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"292 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133380158","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: 14
Detecting tightness via open book decompositions 通过开卷分解检测松紧度
Geometry and Topology Monographs Pub Date : 2015-12-29 DOI: 10.2140/GTM.2015.19.291
Andy Wand
{"title":"Detecting tightness via open book decompositions","authors":"Andy Wand","doi":"10.2140/GTM.2015.19.291","DOIUrl":"https://doi.org/10.2140/GTM.2015.19.291","url":null,"abstract":"Abstract \u0000This article is an expository overview of work by the author characterizing tightness of a closed contact 33–manifold in terms of arbitrary open book decompositions thereof. The intent is to provide a “user’s guide” of the theory.","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124413366","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
Symplectic 4–manifolds, Stein domains, Seiberg–Witten theory and mapping class groups 辛4流形，Stein定义域，Seiberg-Witten理论和映射类群
Geometry and Topology Monographs Pub Date : 2015-12-29 DOI: 10.2140/GTM.2015.19.173
A. Stipsicz
{"title":"Symplectic 4–manifolds, Stein domains, Seiberg–Witten theory and mapping class groups","authors":"A. Stipsicz","doi":"10.2140/GTM.2015.19.173","DOIUrl":"https://doi.org/10.2140/GTM.2015.19.173","url":null,"abstract":"It is less transparent how mapping class groups are related to 4–dimensional topology. By results of Donaldson and Gompf, closed symplectic manifolds (admitting Lefschetz fibration or Lefschetz pencil structures) give rise to various objects in mapping class groups, and therefore the study of these groups has implications to 4–dimensional symplectic topology. There are also converse results; there are 4–dimensional topological theorems that have implications to mapping class group theory. For compact 4–manifolds with nonempty boundary a very similar correspondence can be set up, provided the manifolds admit Stein structures and we consider mapping class groups of surfaces with nonempty boundary.","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133471653","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
Monoids in the mapping class group 映射类组中的Monoids
Geometry and Topology Monographs Pub Date : 2015-04-08 DOI: 10.2140/GTM.2015.19.319
John B. Etnyre, Jeremy Van Horn-Morris
{"title":"Monoids in the mapping class group","authors":"John B. Etnyre, Jeremy Van Horn-Morris","doi":"10.2140/GTM.2015.19.319","DOIUrl":"https://doi.org/10.2140/GTM.2015.19.319","url":null,"abstract":"In this article we survey, and make a few new observations about, the surprising connection between sub-monoids of the mapping class groups and interesting geometry and topology in low-dimensions. 57R17; 20F36","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124528590","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: 19
Open book decompositions versus prime factorizations of closed, oriented 3-manifolds 开卷分解与封闭定向3流形的质因数分解
Geometry and Topology Monographs Pub Date : 2014-07-08 DOI: 10.2140/GTM.2015.19.145
P. Ghiggini, P. Lisca
{"title":"Open book decompositions versus prime factorizations of closed, oriented 3-manifolds","authors":"P. Ghiggini, P. Lisca","doi":"10.2140/GTM.2015.19.145","DOIUrl":"https://doi.org/10.2140/GTM.2015.19.145","url":null,"abstract":"Let M be a closed, oriented, connected 3–manifold and .B; / an open book decomposition on M with page † and monodromy ' . It is easy to see that the first Betti number of † is bounded below by the number of S S –factors in the prime factorization of M . Our main result is that equality is realized if and only if ' is trivial and M is a connected sum of copies of S S . We also give some applications of our main result, such as a new proof of the fact that if the closure of a braid with n strands is the unlink with n components then the braid is trivial.","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132734530","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
Sections of surface bundles 表面束截面
Geometry and Topology Monographs Pub Date : 2013-09-15 DOI: 10.2140/gtm.2015.19.1
J. Hillman
{"title":"Sections of surface bundles","authors":"J. Hillman","doi":"10.2140/gtm.2015.19.1","DOIUrl":"https://doi.org/10.2140/gtm.2015.19.1","url":null,"abstract":"A bundle with base $B$ and fibre $F$ aspherical closed surfaces has a section if and only if the action $:pi_1(B)to{Out}(pi_1(F))$ factors through $Aut(pi_1(F))$ and a cohomology class is 0. We simplify and make more explicit the latter condition. We also show that the transgression $d^2_{2,0}$ in the homology LHS spectral sequence of a central extension is evaluation of the extension class. Examples with hyperbolic fibre and no section (based on ideas of Endo) added.","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"02 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130642759","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: 9
Kernel(J) warns of false vacua Kernel(J)警告假真空
Geometry and Topology Monographs Pub Date : 2011-10-19 DOI: 10.2140/GTM.2012.18.91
M. Freedman
{"title":"Kernel(J) warns of false vacua","authors":"M. Freedman","doi":"10.2140/GTM.2012.18.91","DOIUrl":"https://doi.org/10.2140/GTM.2012.18.91","url":null,"abstract":"J H C Whitehead defined a map Jr W r .SO/! s r from the homotopy of the special orthogonal group to the stable homotopy of spheres. Within a toy model we show how the known computation for kernel.J / leads to nonlinear –models with spherical source (space) and spherical target which admit false vacua separated from the true vacuum by an energy barrier. In this construction, the dimension of space must be at least 8 and the dimension of the –model target at least 5 .","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123349685","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
Khovanov homology and gauge theory Khovanov同调与规范理论
Geometry and Topology Monographs Pub Date : 2011-08-15 DOI: 10.2140/GTM.2012.18.291
E. Witten
{"title":"Khovanov homology and gauge theory","authors":"E. Witten","doi":"10.2140/GTM.2012.18.291","DOIUrl":"https://doi.org/10.2140/GTM.2012.18.291","url":null,"abstract":"In these notes, I will sketch a new approach to Khovanov homology of knots and links based on counting the solutions of certain elliptic partial differential equations in four and five dimensions. The equations are formulated on four and five-dimensional manifolds with boundary, with a rather subtle boundary condition that encodes the knots and links. The construction is formally analogous to Floer and Donaldson theory in three and four dimensions. It was discovered using quantum field theory arguments but can be described and understood purely in terms of classical gauge theory.","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124437160","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: 69
Topological logarithmic structures 拓扑对数结构
Geometry and Topology Monographs Pub Date : 2009-07-04 DOI: 10.2140/GTM.2009.16.401
J. Rognes
{"title":"Topological logarithmic structures","authors":"J. Rognes","doi":"10.2140/GTM.2009.16.401","DOIUrl":"https://doi.org/10.2140/GTM.2009.16.401","url":null,"abstract":"A logarithmic structure on a commutative ring A is a commutative monoid M with a homomorphism to the underlying multiplicative monoid of A. This determines a localization AŒM  of A. In algebro-geometric terms, we might say that M cuts out a divisor D from Spec.A/, and AŒM  is the ring of regular functions on the open complement. In general the logarithmic structure carries more information than the localization. For example, the Kahler differentials of A form an A–module  A , generated by differentials of the form da, which are globally defined over Spec.A/. The Kahler differentials of the localization form the AŒM –module  AŒM  , which also contains differentials of the form m da, having poles of arbitrary degree along D . The logarithmic structure specifies an intermediate A–module of logarithmic Kahler differentials,  .A;M / , generated by differentials of the form da and d log mDm dm, having only poles of simple, or logarithmic, type along D . The logarithmic structure is therefore a more moderate way of specifying a localization than the actual localized ring. See Kato [35] and Illusie [34] for introductions to logarithmic algebraic geometry.","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125719986","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: 32
On the number of optimal surfaces 最优曲面的个数
Geometry and Topology Monographs Pub Date : 2009-04-12 DOI: 10.2140/gtm.2008.14.557
A. Vdovina
{"title":"On the number of optimal surfaces","authors":"A. Vdovina","doi":"10.2140/gtm.2008.14.557","DOIUrl":"https://doi.org/10.2140/gtm.2008.14.557","url":null,"abstract":"Let X be a closed oriented Riemann surface of genus 2 of constant negative curvature 1. A surface containing a disk of maximal radius is an optimal surface. This paper gives exact formulae for the number of optimal surfaces of genus 4 up to orientation-preserving isometry. We show that the automorphism group of such a surface is always cyclic of order 1, 2, 3 or 6. We also describe a combinatorial structure of nonorientable hyperbolic optimal surfaces.","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131204456","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: 3
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