Twisted linking numbers via representations of fundamental groups

Kenichi Kawagoe

Vol. 205 (2002), No. 1, 139–152

DOI: 10.2140/pjm.2002.205.139

Abstract

Using representations of fundamental groups, we introduce the concept of twisted linking numbers. If the corresponding representation is trivial, the twisted linking number coincides with the linking number. In the case of a nontrivial representation, however, this is not necessarily true, which implies that the twisted linking number can detect the nontriviality of an embedding of 𝕊¹. An example is given for which the linking number is trivial but the twisted linking number is not.

Milestones

Received: 27 September 2000

Revised: 11 October 2001

Published: 1 July 2002