Homology Invariants

Author:

Hartley Richard,Murasugi Kunio

Abstract

There have been few published results concerning the relationship between the homology groups of branched and unbranched covering spaces of knots, despite the fact that these invariants are such powerful invariants for distinguishing knot types and have long been recognised as such [8]. It is well known that a simple relationship exists between these homology groups for cyclic covering spaces (see Example 3 in § 3), however for more complicated covering spaces, little has previously been known about the homology group, H1(M) of the branched covering space or about H1(U), U being the corresponding unbranched covering space, or about the relationship between these two groups.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 11 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. An explicit relation between knot groups in lens spaces and those in S3;Journal of Knot Theory and Its Ramifications;2018-07

2. A note on Riley polynomials of 2-bridge knots;Annales de la Faculté des sciences de Toulouse : Mathématiques;2017-12-14

3. Epimorphisms of knot groups onto free products;Topology;2003-11

4. How hyperbolic knots with homeomorphic cyclic branched coverings are related;Topology and its Applications;2002-06

5. Homologically trivial actions on cyclic coverings of knots;Pacific Journal of Mathematics;1999-03-01

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