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Indexed by:期刊论文

Date of Publication:2015-01-01

Journal:Communications in Mathematics and Statistics

Included Journals:Scopus

Volume:3

Issue:4

Page Number:497-526

ISSN No.:21946701

Abstract: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. ? 2015, School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag Berlin Heidelberg.