Fibred knots and twisted Alexander invariants

By J. Cha. 2001

64 citations recorded by the source corpus.

We study the twisted Alexander invariants of fibred knots. We establish necessary conditions on the twisted Alexander invariants for a knot to be fibred, and develop a practical method to compute the twisted Alexander invariants from the homotopy type of a monodromy. It is illustrated that the twisted Alexander invariants carry more information on fibredness than the classical Alexander invariants, even for knots with trivial Alexander polynomials.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eec629e5b9d8aff249d1dbb32428c81a85092c26

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The Thurston norm, fibered manifolds and twisted Alexander polynomials (2005, background): “Given a representation π1(M) → GL(R, k) Cha [1] defined a twisted Alexander polynomial ∆α1 (t) ∈ R[t ±1 ], which is well-defined up to multiplication by a unit in R[t±1].”
A SURVEY OF TWISTED ALEXANDER POLYNOMIALS (2009, methodology): “−1}. A direct calculation using [Tu01, Theorem 2.2] now shows that τ(N,γ⊗φ) ∈ Q(t) is monic and that deg(τ(N,γ⊗φ)) = −kχ(S) = k||φ||T. A SURVEY OF TWISTED ALEXANDER POLYNOMIALS 21 The calculations in [Ch03], [GKM05] and [FK06] gave evidence that twisted Alexander polynomials are very successful at d”
Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation (2008, background): “The theory and application of twisted knot polynomials has been considered by many authors; a few papers include [3,10,12,14,15,17,25,26,37].”