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

作　　者：Fuquan Fang Fengchun Lei Jie Wu 

机构地区：[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

出　　处：《Communications in Mathematics and Statistics》2015年第4期497-526,共30页数学与统计通讯（英文）

基　　金：The authors would like to thank Joan Birman and Haynes Miller for their encouragements and helpful suggestions on this project.Fuquan Fang and Fengchun Lei supported in part by a Key Grant(No.11431009);an Overseas-Collaboration Grant(No.11329101)of NSFC of China;Research is supported by the Singapore Ministry of Education research Grant(AcRF Tier 1 WBS No.R-146-000-190-112)and a Grant(No.11329101)of NSFC of China.

摘　　要：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 themeridians excluding themeridian 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.

关 键 词：Homotopy groups Link groups Symmetric commutator subgroups Intersection subgroups Link invariants Brunnian-type links Strongly non-splittable links 

分 类 号：O17[理学—数学]