Twisted Alexander invariants of knot group representations

Takefumi Nosaka

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arXiv · 2002.10192

Twisted Alexander invariants of knot group representations

Takefumi Nosaka

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Abstract

Given a homomorphism from a knot group to a fixed group, we introduce an element of a $K_1$-group, which is a generalization of (twisted) Alexander polynomials. We compare this $K_1$-class with other Alexander polynomials. In terms of semi-local rings, we compute the $K_1$-classes of some knots and show their non-triviality. We also introduce metabelian Alexander polynomials.

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Takefumi Nosaka. 2020-02-24. Twisted Alexander invariants of knot group representations. https://arxiv.org/abs/2002.10192

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