Fibred knots and twisted Alexander invariants
Geometric Topology
2007-05-23 v2
Abstract
We introduce a new algebraic topological technique to detect non-fibred knots in the three sphere using the twisted Alexander invariants. As an application, we show that for any Seifert matrix of a knot with a nontrivial Alexander polynomial, there exist infinitely many non-fibered knots with the given Seifert matrix. We illustrate examples of knots that have trivial Alexander polynomials but do not have twisted Alexander invariants of fibred knots.
Cite
@article{arxiv.math/0109136,
title = {Fibred knots and twisted Alexander invariants},
author = {Jae Choon Cha},
journal= {arXiv preprint arXiv:math/0109136},
year = {2007}
}
Comments
14 pages, 5 figures; minor modification, reference addition, and address change