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On the twisted K-homology of simple Lie groups 单李群的扭曲k -同调
Topology Pub Date : 2006-11-01 Epub Date: 2006-08-21 DOI: 10.1016/j.top.2006.06.007
Christopher L. Douglas
{"title":"On the twisted K-homology of simple Lie groups","authors":"Christopher L. Douglas","doi":"10.1016/j.top.2006.06.007","DOIUrl":"10.1016/j.top.2006.06.007","url":null,"abstract":"<div><p>We prove that the twisted <span><math><mi>K</mi></math></span>-homology of a simply connected simple Lie group <span><math><mi>G</mi></math></span> of rank <span><math><mi>n</mi></math></span> is an exterior algebra on <span><math><mi>n</mi><mo>−</mo><mn>1</mn></math></span> generators tensor a cyclic group. We give a detailed description of the order of this cyclic group in terms of the dimensions of irreducible representations of <span><math><mi>G</mi></math></span> and show that the congruences determining this cyclic order lift along the twisted index map to relations in the twisted <span><math><msup><mrow><mstyle><mi>Spin</mi></mstyle></mrow><mrow><mi>c</mi></mrow></msup></math></span> bordism group of <span><math><mi>G</mi></math></span>.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 6","pages":"Pages 955-988"},"PeriodicalIF":0.0,"publicationDate":"2006-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.06.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188079","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: 56
Deforming the R-Fuchsian (4, 4, 4)-triangle group into a lattice 将R-Fuchsian(4,4,4)三角形群变形为晶格
Topology Pub Date : 2006-11-01 Epub Date: 2006-07-21 DOI: 10.1016/j.top.2006.06.005
Martin Deraux
{"title":"Deforming the R-Fuchsian (4, 4, 4)-triangle group into a lattice","authors":"Martin Deraux","doi":"10.1016/j.top.2006.06.005","DOIUrl":"10.1016/j.top.2006.06.005","url":null,"abstract":"<div><p>We prove that the last discrete deformation of the <span><math><mi>R</mi></math></span>-Fuchsian (4, 4, 4)-triangle group in <span><math><mi>P</mi><mi>U</mi><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> is a cocompact arithmetic lattice. We also describe an experimental method for finding the combinatorics of a Dirichlet fundamental domain, and apply it to the lattice in question.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 6","pages":"Pages 989-1020"},"PeriodicalIF":0.0,"publicationDate":"2006-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.06.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188055","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
The Thurston norm, fibered manifolds and twisted Alexander polynomials 瑟斯顿范数，纤维流形和扭曲亚历山大多项式
Topology Pub Date : 2006-11-01 Epub Date: 2006-07-18 DOI: 10.1016/j.top.2006.06.003
Stefan Friedl , Taehee Kim
{"title":"The Thurston norm, fibered manifolds and twisted Alexander polynomials","authors":"Stefan Friedl ,&nbsp;Taehee Kim","doi":"10.1016/j.top.2006.06.003","DOIUrl":"10.1016/j.top.2006.06.003","url":null,"abstract":"<div><p>Every element in the first cohomology group of a 3-manifold is dual to embedded surfaces. The Thurston norm measures the minimal ‘complexity’ of such surfaces. For instance the Thurston norm of a knot complement determines the genus of the knot in the 3-sphere. We show that the degrees of twisted Alexander polynomials give lower bounds on the Thurston norm, generalizing work of McMullen and Turaev. Our bounds attain their most concise form when interpreted as the degrees of the Reidemeister torsion of a certain twisted chain complex. We show that these lower bounds give the correct genus bounds for all knots with 12 crossings or less, including the Conway knot and the Kinoshita–Terasaka knot which have trivial Alexander polynomial.</p><p>We also give obstructions to fibering 3-manifolds using twisted Alexander polynomials and detect all knots with 12 crossings or less that are not fibered. For some of these it was unknown whether or not they are fibered. Our work in particular extends the fibering obstructions of Cha to the case of closed manifolds.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 6","pages":"Pages 929-953"},"PeriodicalIF":0.0,"publicationDate":"2006-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.06.003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188045","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: 97
Bordism invariants of the mapping class group 映射类组的秩不变量
Topology Pub Date : 2006-09-01 Epub Date: 2006-07-24 DOI: 10.1016/j.top.2006.06.001
Aaron Heap
{"title":"Bordism invariants of the mapping class group","authors":"Aaron Heap","doi":"10.1016/j.top.2006.06.001","DOIUrl":"10.1016/j.top.2006.06.001","url":null,"abstract":"<div><p>We define new bordism and spin bordism invariants of certain subgroups of the mapping class group of a surface. In particular, they are invariants of the Johnson filtration of the mapping class group. The second and third terms of this filtration are the well-known Torelli group and Johnson subgroup, respectively. We introduce a new representation in terms of spin bordism, and we prove that this single representation contains all of the information given by the Johnson homomorphism, the Birman–Craggs homomorphism, and the Morita homomorphism.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 5","pages":"Pages 851-886"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.06.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188019","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: 19
The Boardman–Vogt resolution of operads in monoidal model categories 一元模型范畴中操作数的Boardman-Vogt解析
Topology Pub Date : 2006-09-01 Epub Date: 2006-07-21 DOI: 10.1016/j.top.2006.05.001
Clemens Berger , Ieke Moerdijk
{"title":"The Boardman–Vogt resolution of operads in monoidal model categories","authors":"Clemens Berger ,&nbsp;Ieke Moerdijk","doi":"10.1016/j.top.2006.05.001","DOIUrl":"10.1016/j.top.2006.05.001","url":null,"abstract":"<div><p>We extend the <span><math><mstyle><mi>W</mi></mstyle></math></span>-construction of Boardman and Vogt to operads of an arbitrary monoidal model category with suitable interval, and show that it provides a cofibrant resolution for well-pointed <span><math><mi>Σ</mi></math></span>-cofibrant operads. The standard simplicial resolution of Godement as well as the cobar–bar chain resolution are shown to be particular instances of this generalised <span><math><mstyle><mi>W</mi></mstyle></math></span>-construction.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 5","pages":"Pages 807-849"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.05.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188003","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: 116
A fake projective plane with an order 7 automorphism 具有7阶自同构的假投影平面
Topology Pub Date : 2006-09-01 Epub Date: 2006-07-26 DOI: 10.1016/j.top.2006.06.006
JongHae Keum
{"title":"A fake projective plane with an order 7 automorphism","authors":"JongHae Keum","doi":"10.1016/j.top.2006.06.006","DOIUrl":"10.1016/j.top.2006.06.006","url":null,"abstract":"<div><p>A fake projective plane is a compact complex surface (a compact complex manifold of dimension 2) with the same Betti numbers as the complex projective plane, but not isomorphic to the complex projective plane. As was shown by Mumford, there exists at least one such surface.</p><p>In this paper we prove the existence of a fake projective plane which is birational to a cyclic cover of degree 7 of a Dolgachev surface.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 5","pages":"Pages 919-927"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.06.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188069","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: 34
A topological view of Gromov–Witten theory Gromov-Witten理论的拓扑学观点
Topology Pub Date : 2006-09-01 Epub Date: 2006-07-20 DOI: 10.1016/j.top.2006.06.002
D. Maulik, R. Pandharipande
{"title":"A topological view of Gromov–Witten theory","authors":"D. Maulik,&nbsp;R. Pandharipande","doi":"10.1016/j.top.2006.06.002","DOIUrl":"10.1016/j.top.2006.06.002","url":null,"abstract":"<div><p>We study relative Gromov–Witten theory via universal relations provided by the degeneration and localization formulas. We find relative Gromov–Witten theory is completely determined by absolute Gromov–Witten theory. The relationship between the relative and absolute theories is guided by a strong analogy to classical topology.</p><p>As an outcome, we present a mathematical determination of the Gromov–Witten invariants (in all genera) of the Calabi–Yau quintic 3-fold in terms of known theories.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 5","pages":"Pages 887-918"},"PeriodicalIF":0.0,"publicationDate":"2006-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.06.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188033","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: 161
Manifolds obtained by surgery on an infinite number of knots in S3 在S3中无限数量的结上手术得到的流形
Topology Pub Date : 2006-07-01 Epub Date: 2006-05-24 DOI: 10.1016/j.top.2006.02.001
John K. Osoinach Jr.
{"title":"Manifolds obtained by surgery on an infinite number of knots in S3","authors":"John K. Osoinach Jr.","doi":"10.1016/j.top.2006.02.001","DOIUrl":"10.1016/j.top.2006.02.001","url":null,"abstract":"<div><p>The construction of 3-manifolds via Dehn surgery on links in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> is an important technique in the classification of 3-manifolds. This paper describes a method of constructing infinite collections of distinct hyperbolic knots in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> which admit a longitudinal surgery yielding the same manifold. In one case, the knots constructed each admit a longitudinal surgery yielding the same hyperbolic manifold; in another case, the knots admit a longitudinal surgery yielding the same toroidal manifold. This answers a question formulated by Kirby in the Kirby problem list [R. Kirby (Ed.), Problems in low-dimensional topology, in: Geometric Topology, American Mathematical Society/International Press, 1997] in the affirmative, which asks if there is a homology 3-sphere, or any 3-manifold, that can be obtained by <span><math><mi>n</mi></math></span> surgery on an infinite number of distinct knots.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 4","pages":"Pages 725-733"},"PeriodicalIF":0.0,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.02.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188442","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: 43
Some examples of free actions on products of spheres 对球体积的自由作用的一些例子
Topology Pub Date : 2006-07-01 Epub Date: 2006-05-09 DOI: 10.1016/j.top.2006.02.002
Ian Hambleton
{"title":"Some examples of free actions on products of spheres","authors":"Ian Hambleton","doi":"10.1016/j.top.2006.02.002","DOIUrl":"https://doi.org/10.1016/j.top.2006.02.002","url":null,"abstract":"<div><p>If <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> are finite groups with periodic Tate cohomology, then <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>×</mo><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> acts freely and smoothly on some product <span><math><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 4","pages":"Pages 735-749"},"PeriodicalIF":0.0,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.02.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137090966","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
On bifurcation braid monodromy of elliptic fibrations 椭圆型纤颤的分岔编织单态
Topology Pub Date : 2006-07-01 Epub Date: 2006-05-05 DOI: 10.1016/j.top.2006.03.001
Michael Lönne
{"title":"On bifurcation braid monodromy of elliptic fibrations","authors":"Michael Lönne","doi":"10.1016/j.top.2006.03.001","DOIUrl":"10.1016/j.top.2006.03.001","url":null,"abstract":"<div><p>We propose to study a new kind of monodromy homomorphism for families of regular elliptic fibrations of a given differentiable fibration type to get a hold on topological properties of moduli stacks of elliptic surfaces.</p><p>In specific cases, including the most significant one, when all singular fibres are nodal irreducible rational curves, we compute the corresponding monodromy group, a subgroup of the mapping class group of the fibration base punctured at the singular values of the fibration.</p><p>We study a tentative algebraic characterisation and give implications for the group of diffeomorphisms compatible with the fibration.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 4","pages":"Pages 785-806"},"PeriodicalIF":0.0,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.03.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188447","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
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