Link Colorability, Covering Spaces and Isotopy
by
Ollie Nanyes
Bradley University

In this paper we use the concepts of link diagram colorability and branched cyclic covering spaces to study links under the piecewise linear isotopy equivalence relation (non-ambient isotopy; local knots are allowed to be tied and removed). We also show that the "nullity corrected" Goeritz matrix of a link, which presents the first homology group of the two fold cyclic branched covering space, determines all possible diagram colorings. However, unlike the case for knots, it does not determine all maps of the link group onto generalized dihedral groups.

Date received: January 26, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # caaa-14.