Fibred knots and twisted Alexander invariants

Details Fibred knots and twisted Alexander invariants Fibred knots and twisted Alexander invariants

2001-09-19

arxiv.org/abs/math/0109136v2

Mathematics

Geometric Topology

14 pages, 5 figures; minor modification, reference addition, and address change

Scientific paper

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.

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