Topology最新文献

筛选
英文 中文
A geometric classification of the path components of the space of locally stable maps S3→R4 局部稳定映射S3→R4空间路径分量的几何分类
Topology Pub Date : 2007-11-01 DOI: 10.1016/j.top.2006.12.004
Ole Andersson
{"title":"A geometric classification of the path components of the space of locally stable maps S3→R4","authors":"Ole Andersson","doi":"10.1016/j.top.2006.12.004","DOIUrl":"10.1016/j.top.2006.12.004","url":null,"abstract":"<div><p>Locally stable maps <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> are classified up to homotopy through locally stable maps. The equivalence class of a map <span><math><mi>f</mi></math></span> is determined by three invariants: the isotopy class <span><math><mi>σ</mi><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow></math></span> of its framed singularity link, the generalized normal degree <span><math><mi>ν</mi><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow></math></span>, and the algebraic number of cusps <span><math><mi>κ</mi><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow></math></span> of any extension of <span><math><mi>f</mi></math></span> to a locally stable map of the 4-disk into <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>5</mn></mrow></msup></math></span>. Relations between the invariants are described, and it is proved that for any <span><math><mi>σ</mi></math></span>, <span><math><mi>ν</mi></math></span>, and <span><math><mi>κ</mi></math></span> which satisfy these relations, there exists a map <span><math><mi>f</mi><mo>:</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>→</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> with <span><math><mi>σ</mi><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow><mo>=</mo><mi>σ</mi></math></span>, <span><math><mi>ν</mi><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow><mo>=</mo><mi>ν</mi></math></span>, and <span><math><mi>κ</mi><mrow><mo>(</mo><mi>f</mi><mo>)</mo></mrow><mo>=</mo><mi>κ</mi></math></span>. It follows in particular that every framed link in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> is the singularity set of some locally stable map into <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 6","pages":"Pages 577-597"},"PeriodicalIF":0.0,"publicationDate":"2007-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.12.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Relative hyperbolicity, classifying spaces, and lower algebraic K-theory 相对双曲,分类空间,和下代数k理论
Topology Pub Date : 2007-11-01 DOI: 10.1016/j.top.2007.03.001
Jean-François Lafont , Ivonne J. Ortiz
{"title":"Relative hyperbolicity, classifying spaces, and lower algebraic K-theory","authors":"Jean-François Lafont ,&nbsp;Ivonne J. Ortiz","doi":"10.1016/j.top.2007.03.001","DOIUrl":"10.1016/j.top.2007.03.001","url":null,"abstract":"<div><p>For <span><math><mi>Γ</mi></math></span> a relatively hyperbolic group, we construct a model for the universal space among <span><math><mi>Γ</mi></math></span>-spaces with isotropy on the family <span><math><mi>V</mi><mi>C</mi></math></span> of virtually cyclic subgroups of <span><math><mi>Γ</mi></math></span>. We provide a recipe for identifying the maximal infinite virtually cyclic subgroups of Coxeter groups which are lattices in <span><math><msup><mrow><mi>O</mi></mrow><mrow><mo>+</mo></mrow></msup><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mstyle><mi>Isom</mi></mstyle><mrow><mo>(</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></math></span>. We use the information we obtain to explicitly compute the lower algebraic <span><math><mi>K</mi></math></span>-theory of the Coxeter group <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> (a non-uniform lattice in <span><math><msup><mrow><mi>O</mi></mrow><mrow><mo>+</mo></mrow></msup><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span>). Part of this computation involves calculating certain Waldhausen Nil-groups for <span><math><mi>Z</mi><mrow><mo>[</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo></mrow></math></span>, <span><math><mi>Z</mi><mrow><mo>[</mo><msub><mrow><mi>D</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>]</mo></mrow></math></span>.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 6","pages":"Pages 527-553"},"PeriodicalIF":0.0,"publicationDate":"2007-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.03.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 29
Reduced Delzant spaces and a convexity theorem 简化Delzant空间和一个凸性定理
Topology Pub Date : 2007-11-01 DOI: 10.1016/j.top.2007.02.007
Bong H. Lian , Bailin Song
{"title":"Reduced Delzant spaces and a convexity theorem","authors":"Bong H. Lian ,&nbsp;Bailin Song","doi":"10.1016/j.top.2007.02.007","DOIUrl":"10.1016/j.top.2007.02.007","url":null,"abstract":"<div><p>The convexity theorem of Atiyah and Guillemin–Sternberg says that any connected compact manifold with Hamiltonian torus action has a moment map whose image is the convex hull of the image of the fixed point set. Sjamaar–Lerman proved that the Marsden–Weinstein reduction of a connected Hamitonian <span><math><mi>G</mi></math></span>-manifold is a stratified symplectic space. Suppose <span><math><mn>1</mn><mo>→</mo><mi>A</mi><mo>→</mo><mi>G</mi><mo>→</mo><mi>T</mi><mo>→</mo><mn>1</mn></math></span> is an exact sequence of compact Lie groups and <span><math><mi>T</mi></math></span> is a torus. Then the reduction of a Hamiltonian <span><math><mi>G</mi></math></span>-manifold with respect to <span><math><mi>A</mi></math></span> yields a Hamiltonian <span><math><mi>T</mi></math></span>-space. We show that if the <span><math><mi>A</mi></math></span>-moment map is proper, then the convexity theorem holds for such a Hamiltonian <span><math><mi>T</mi></math></span>-space, even when it is singular. We also prove that if, furthermore, the <span><math><mi>T</mi></math></span>-space has dimension <span><math><mn>2</mn><mstyle><mi>dim</mi></mstyle><mspace></mspace><mi>T</mi></math></span> and <span><math><mi>T</mi></math></span> acts effectively, then the moment polytope is sufficient to essentially distinguish their homeomorphism type, though not their diffeomorphism types. This generalizes a theorem of Delzant in the smooth case. This paper is a concise version of a companion paper [B. Lian. B. Song, A convexity theorem and reduced Delzant spaces, <span>math.DG/0509429</span><svg><path></path></svg>].</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 6","pages":"Pages 554-576"},"PeriodicalIF":0.0,"publicationDate":"2007-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.02.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Publication information 发布信息
Topology Pub Date : 2007-11-01 DOI: 10.1016/S0040-9383(07)00069-9
{"title":"Publication information","authors":"","doi":"10.1016/S0040-9383(07)00069-9","DOIUrl":"https://doi.org/10.1016/S0040-9383(07)00069-9","url":null,"abstract":"","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 6","pages":"Page IFC"},"PeriodicalIF":0.0,"publicationDate":"2007-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0040-9383(07)00069-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91974838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The homotopy type of the complement of a coordinate subspace arrangement 一坐标子空间排列的补的同伦类型
Topology Pub Date : 2007-09-01 DOI: 10.1016/j.top.2007.02.006
Jelena Grbić, Stephen Theriault
{"title":"The homotopy type of the complement of a coordinate subspace arrangement","authors":"Jelena Grbić,&nbsp;Stephen Theriault","doi":"10.1016/j.top.2007.02.006","DOIUrl":"10.1016/j.top.2007.02.006","url":null,"abstract":"<div><p>The homotopy type of the complement of a complex coordinate subspace arrangement is studied by utilising some connections between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy equivalent to a wedge of spheres is described. One consequence is an application in commutative algebra: certain local rings are proved to be Golod, that is, all Massey products in their homology vanish.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 4","pages":"Pages 357-396"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.02.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"93385344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 91
Information for Authors 作者信息
Topology Pub Date : 2007-09-01 DOI: 10.1016/S0040-9383(07)00052-3
{"title":"Information for Authors","authors":"","doi":"10.1016/S0040-9383(07)00052-3","DOIUrl":"https://doi.org/10.1016/S0040-9383(07)00052-3","url":null,"abstract":"","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 5","pages":"Page IFC"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S0040-9383(07)00052-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137284895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Exceptional Dehn fillings on hyperbolic 3-manifolds with at least two boundary components 具有至少两个边界分量的双曲3-流形上的例外Dehn填充
Topology Pub Date : 2007-09-01 DOI: 10.1016/j.top.2007.03.003
Sangyop Lee
{"title":"Exceptional Dehn fillings on hyperbolic 3-manifolds with at least two boundary components","authors":"Sangyop Lee","doi":"10.1016/j.top.2007.03.003","DOIUrl":"10.1016/j.top.2007.03.003","url":null,"abstract":"<div><p>We estimate the number of exceptional slopes for hyperbolic 3-manifolds with a torus boundary component and at least one other boundary component.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 5","pages":"Pages 437-468"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.03.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Three models for the homotopy theory of homotopy theories 同伦理论中的同伦理论的三个模型
Topology Pub Date : 2007-09-01 DOI: 10.1016/j.top.2007.03.002
Julia E. Bergner
{"title":"Three models for the homotopy theory of homotopy theories","authors":"Julia E. Bergner","doi":"10.1016/j.top.2007.03.002","DOIUrl":"10.1016/j.top.2007.03.002","url":null,"abstract":"<div><p>Given any model category, or more generally any category with weak equivalences, its simplicial localization is a simplicial category which can rightfully be called the “homotopy theory” of the model category. There is a model category structure on the category of simplicial categories, so taking its simplicial localization yields a “homotopy theory of homotopy theories”. In this paper we show that there are two different categories of diagrams of simplicial sets, each equipped with an appropriate definition of weak equivalence, such that the resulting homotopy theories are each equivalent to the homotopy theory arising from the model category structure on simplicial categories. Thus, any of these three categories with the respective weak equivalences could be considered a model for the homotopy theory of homotopy theories. One of them in particular, Rezk’s complete Segal space model category structure on the category of simplicial spaces, is much more convenient from the perspective of making calculations and therefore obtaining information about a given homotopy theory.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 4","pages":"Pages 397-436"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.03.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 147
Homology at infinity; fractal geometry of limiting symbols for modular subgroups 无穷远处的同调;模子群极限符号的分形几何
Topology Pub Date : 2007-09-01 DOI: 10.1016/j.top.2007.03.004
M. Kesseböhmer , B.O. Stratmann
{"title":"Homology at infinity; fractal geometry of limiting symbols for modular subgroups","authors":"M. Kesseböhmer ,&nbsp;B.O. Stratmann","doi":"10.1016/j.top.2007.03.004","DOIUrl":"10.1016/j.top.2007.03.004","url":null,"abstract":"<div><p>In this paper we use fractal geometry to investigate boundary aspects of the first homology group for finite coverings of the modular surface. We obtain a complete description of algebraically invisible parts of this homology group. More precisely, we first show that for any modular subgroup the geodesic forward dynamic on the associated surface admits a canonical symbolic representation by a finitely irreducible shift space. We then use this representation to derive a complete multifractal description of the higher-dimensional level sets arising from the Manin–Marcolli limiting modular symbols.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 5","pages":"Pages 469-491"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.03.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
The tangential end fibration of an aspherical Poincaré complex 非球面poincarcarcars复合物的切向端纤维化
Topology Pub Date : 2007-09-01 DOI: 10.1016/j.top.2007.01.004
Yanghyun Byun
{"title":"The tangential end fibration of an aspherical Poincaré complex","authors":"Yanghyun Byun","doi":"10.1016/j.top.2007.01.004","DOIUrl":"10.1016/j.top.2007.01.004","url":null,"abstract":"<div><p>We construct a sphere fibration over a finite aspherical Poincaré complex <span><math><mi>X</mi></math></span>, which we call the tangential end fibration, under the condition that the universal cover of <span><math><mi>X</mi></math></span> is forward tame and simply connected at infinity. We show that it is tangent to <span><math><mi>X</mi></math></span> if the formal dimension of <span><math><mi>X</mi></math></span> is even or, when the formal dimension is odd, if the diagonal <span><math><mi>X</mi><mo>→</mo><mi>X</mi><mo>×</mo><mi>X</mi></math></span> admits a Poincaré embedding structure.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"46 5","pages":"Pages 507-525"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.01.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信