TopologyPub Date : 2006-07-01DOI: 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}
TopologyPub Date : 2006-07-01DOI: 10.1016/j.top.2006.03.002
Baris Coskunuzer
{"title":"Uniform 1-cochains and genuine laminations","authors":"Baris Coskunuzer","doi":"10.1016/j.top.2006.03.002","DOIUrl":"10.1016/j.top.2006.03.002","url":null,"abstract":"<div><p>We construct a pair of transverse genuine laminations on an atoroidal 3-manifold admitting a transversely orientable uniform 1-cochain. The laminations are induced by the uniform 1-cochain and they are the <em>straightening</em> of the coarse laminations defined by Calegari, by using minimal surface techniques. Moreover, when we collapse these laminations, we get a topological pseudo-Anosov flow, as defined by Mosher.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 4","pages":"Pages 751-784"},"PeriodicalIF":0.0,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.03.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188454","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}
TopologyPub Date : 2006-07-01DOI: 10.1016/j.top.2006.01.005
Boju Jiang , Yi Ni , Shicheng Wang , Qing Zhou
{"title":"Embedding infinite cyclic covers of knot spaces into 3-space","authors":"Boju Jiang , Yi Ni , Shicheng Wang , Qing Zhou","doi":"10.1016/j.top.2006.01.005","DOIUrl":"10.1016/j.top.2006.01.005","url":null,"abstract":"<div><p>We say a knot <span><math><mi>k</mi></math></span> in the 3-sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> has <em>Property</em> <span><math><mi>I</mi><mi>E</mi></math></span> if the infinite cyclic cover of the knot exterior embeds into <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. Clearly all fibred knots have Property <span><math><mi>I</mi><mi>E</mi></math></span>.</p><p>There are infinitely many non-fibred knots with Property <span><math><mi>I</mi><mi>E</mi></math></span> and infinitely many non-fibred knots without property <span><math><mi>I</mi><mi>E</mi></math></span>. Both kinds of examples are established here for the first time. Indeed we show that if a genus 1 non-fibred knot has Property <span><math><mi>I</mi><mi>E</mi></math></span>, then its Alexander polynomial <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></math></span> must be either 1 or <span><math><mn>2</mn><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>5</mn><mi>t</mi><mo>+</mo><mn>2</mn></math></span>, and we give two infinite families of non-fibred genus 1 knots with Property <span><math><mi>I</mi><mi>E</mi></math></span> and having <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn></math></span> and <span><math><mn>2</mn><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>5</mn><mi>t</mi><mo>+</mo><mn>2</mn></math></span> respectively.</p><p>Hence among genus 1 non-fibred knots, no alternating knot has Property <span><math><mi>I</mi><mi>E</mi></math></span>, and there is only one knot with Property <span><math><mi>I</mi><mi>E</mi></math></span> up to ten crossings.</p><p>We also give an obstruction to embedding infinite cyclic covers of a compact 3-manifold into any compact 3-manifold.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 4","pages":"Pages 691-705"},"PeriodicalIF":0.0,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.01.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55188424","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}
TopologyPub Date : 2006-05-01DOI: 10.1016/j.top.2005.11.004
Kári Ragnarsson
{"title":"Alternative stable homotopy classification of BGp∧","authors":"Kári Ragnarsson","doi":"10.1016/j.top.2005.11.004","DOIUrl":"10.1016/j.top.2005.11.004","url":null,"abstract":"<div><p>We give an alternative to the stable classification of <em>p</em>-completed homotopy types of classifying spaces of finite groups offered by Martino–Priddy. For a finite group <em>G</em> with Sylow subgroup <em>S</em>, we regard the stable <em>p</em>-completed classifying space <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mo>∞</mo></mrow></msup><msubsup><mrow><mi>BG</mi></mrow><mrow><mi>p</mi></mrow><mrow><mo>∧</mo></mrow></msubsup></math></span> as an object under <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mo>∞</mo></mrow></msup><mi>BS</mi></math></span> via the canonical inclusion map. Thus we get a classification in terms of induced fusion systems. Applying Oliver's solution to the Martino–Priddy conjecture, we obtain the surprising result that the unstable homotopy type of <span><math><msubsup><mrow><mi>BG</mi></mrow><mrow><mi>p</mi></mrow><mrow><mo>∧</mo></mrow></msubsup></math></span> is determined by the map <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mo>∞</mo></mrow></msup><mi>BS</mi><mo>→</mo><msup><mrow><mi>Σ</mi></mrow><mrow><mo>∞</mo></mrow></msup><msubsup><mrow><mi>BG</mi></mrow><mrow><mi>p</mi></mrow><mrow><mo>∧</mo></mrow></msubsup></math></span>, but not by the homotopy type of <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mo>∞</mo></mrow></msup><msubsup><mrow><mi>BG</mi></mrow><mrow><mi>p</mi></mrow><mrow><mo>∧</mo></mrow></msubsup></math></span>.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 3","pages":"Pages 601-609"},"PeriodicalIF":0.0,"publicationDate":"2006-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2005.11.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55187891","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}
TopologyPub Date : 2006-05-01DOI: 10.1016/j.top.2005.11.005
Taehee Kim
{"title":"New obstructions to doubly slicing knots","authors":"Taehee Kim","doi":"10.1016/j.top.2005.11.005","DOIUrl":"10.1016/j.top.2005.11.005","url":null,"abstract":"<div><p>A knot in the 3-sphere is called doubly slice if it is a slice of an unknotted 2-sphere in the 4-sphere. We give a bi-sequence of new obstructions for a knot being doubly slice. We construct it following the idea of Cochran-Orr-Teichner's filtration of the classical knot concordance group. This yields a bi-filtration of the monoid of knots (under the connected sum operation) indexed by pairs of half integers. Doubly slice knots lie in the intersection of this bi-filtration. We construct examples of knots which illustrate the non-triviality of this bi-filtration at all levels. In particular, these are new examples of algebraically doubly slice knots that are not doubly slice, and many of these knots are slice. Cheeger-Gromov's von Neumann rho invariants play a key role to show non-triviality of this bi-filtration. We also show some classical invariants are reflected at the initial levels of this bi-filtration, and obtain a bi-filtration of the double concordance group.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 3","pages":"Pages 543-566"},"PeriodicalIF":0.0,"publicationDate":"2006-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2005.11.005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55187908","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}
TopologyPub Date : 2006-05-01DOI: 10.1016/j.top.2006.01.004
K. Guruprasad, A. Haefliger
{"title":"Closed geodesics on orbifolds","authors":"K. Guruprasad, A. Haefliger","doi":"10.1016/j.top.2006.01.004","DOIUrl":"10.1016/j.top.2006.01.004","url":null,"abstract":"<div><p>In this paper, we try to generalize to the case of compact Riemannian orbifolds <em>Q</em> some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds <em>M</em>. We shall also consider the problem of the existence of infinitely many geometrically distinct closed geodesics.</p><p>In the classical case the solution of those problems involve the consideration of the homotopy groups of <em>M</em> and the homology properties of the free loop space on <em>M</em> (Morse theory). Those notions have their analogue in the case of orbifolds. The main part of this paper will be to recall those notions and to show how the classical techniques can be adapted to the case of orbifolds.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 3","pages":"Pages 611-641"},"PeriodicalIF":0.0,"publicationDate":"2006-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.01.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55187985","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}
TopologyPub Date : 2006-05-01DOI: 10.1016/j.top.2005.06.006
M. Farber , D. Schütz
{"title":"Closed 1-forms with at most one zero","authors":"M. Farber , D. Schütz","doi":"10.1016/j.top.2005.06.006","DOIUrl":"10.1016/j.top.2005.06.006","url":null,"abstract":"<div><p>We prove that in any nonzero cohomology class <span><math><mi>ξ</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>M</mi><mo>;</mo><mi>R</mi><mo>)</mo></math></span> there always exists a closed 1-form having at most one zero.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 3","pages":"Pages 465-473"},"PeriodicalIF":0.0,"publicationDate":"2006-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2005.06.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55187730","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}
TopologyPub Date : 2006-05-01DOI: 10.1016/j.top.2005.09.001
Bertrand Deroin
{"title":"Examples of almost-holomorphic and totally real laminations in complex surfaces","authors":"Bertrand Deroin","doi":"10.1016/j.top.2005.09.001","DOIUrl":"10.1016/j.top.2005.09.001","url":null,"abstract":"<div><p>We show that there exists a Lipschitz almost-complex structure <em>J</em> on <span><math><mi>C</mi><msup><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, arbitrarily close to the standard one, and a compact lamination by <em>J</em>-holomorphic curves satisfying the following properties: it is minimal, it has hyperbolic holonomy and it is transversally Lipschitz. Its transverse Hausdorff dimension can be any number <span><math><mi>δ</mi></math></span> in an interval <span><math><mo>(</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>δ</mi></mrow><mrow><mi>max</mi></mrow></msub><mo>)</mo></math></span> where <span><math><msub><mrow><mi>δ</mi></mrow><mrow><mi>max</mi></mrow></msub><mo>=</mo><mn>1.6309</mn><mo>…</mo><mspace></mspace></math></span>. We also show that there is a compact lamination by totally real surfaces in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> with the same properties, unless the transverse dimension can be any number <span><math><mn>0</mn><mo><</mo><mi>δ</mi><mo><</mo><mn>1</mn></math></span>. Our laminations are transversally totally disconnected.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 3","pages":"Pages 495-512"},"PeriodicalIF":0.0,"publicationDate":"2006-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2005.09.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55187829","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}
TopologyPub Date : 2006-05-01DOI: 10.1016/j.top.2005.06.004
Daniel T. Wise
{"title":"Subgroup separability of the figure 8 knot group","authors":"Daniel T. Wise","doi":"10.1016/j.top.2005.06.004","DOIUrl":"10.1016/j.top.2005.06.004","url":null,"abstract":"<div><p>It is shown that the fundamental groups of certain non-positively curved 2-complexes have the property that their quasiconvex subgroups are the intersections of finite index subgroups.</p><p>As a consequence, every geometrically finite subgroup of the figure 8 knot group is the intersection of finite index subgroups. The same result holds for many other prime alternating link groups.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 3","pages":"Pages 421-463"},"PeriodicalIF":0.0,"publicationDate":"2006-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2005.06.004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55187700","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}
TopologyPub Date : 2006-05-01DOI: 10.1016/j.top.2005.11.001
Mikami Hirasawa , Masakazu Teragaito
{"title":"Crosscap numbers of 2-bridge knots","authors":"Mikami Hirasawa , Masakazu Teragaito","doi":"10.1016/j.top.2005.11.001","DOIUrl":"10.1016/j.top.2005.11.001","url":null,"abstract":"<div><p>We present a practical algorithm to determine the minimal genus of non-orientable spanning surfaces for 2-bridge knots, called the crosscap numbers. We will exhibit a table of crosscap numbers of 2-bridge knots up to 12 crossings (all 362 of them).</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 3","pages":"Pages 513-530"},"PeriodicalIF":0.0,"publicationDate":"2006-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2005.11.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"55187852","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}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
