The Symmetric Commutator Homology of Link Towers and Homotopy Groups of 3-Manifolds

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• 作者：Fuquan Fang ; Fengchun Lei ; Jie Wu
• 关键词：Homotopy groups ; Link groups ; Symmetric commutator subgroups ; Intersection subgroups ; Link invariants ; Brunnian ; type links ; Strongly non ; splittable links ; 55Q40 ; 57M25 ; 55Q20 ; 20F65
• 刊名：Communications in Mathematics and Statistics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：3
• 期：4
• 页码：497-526
• 全文大小：618 KB
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• 作者单位：Fuquan Fang (1)
  Fengchun Lei (2)
  Jie Wu (3)
  
  1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China
  2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China
  3. Department of Mathematics, National University of Singapore, Singapore, 119260, Republic of Singapore
  
• 刊物主题：Mathematics, general; Statistics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：2194-671X

文摘

A link tower is a sequence of links with the structure given by removing the last components. Given a link tower, we prove that there is a chain complex consisting of (non-abelian) groups given by the symmetric commutator subgroup of the normal closures in the link group of the meridians excluding the meridian of the last component with the differential induced by removing the last component. Moreover, the homology groups of these naturally constructed chain complexes are isomorphic to the homotopy groups of the manifold M under certain hypothesis. These chain complexes have canonical quotient abelian chain complexes in Minor’s homotopy link groups with their homologies detecting certain differences of the homotopy link groups in the towers. Keywords Homotopy groups Link groups Symmetric commutator subgroups Intersection subgroups Link invariants Brunnian-type links Strongly non-splittable links