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Twisted Alexander invariants of knot group representations

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arxiv 2002.10192 v3 pith:JUPSJE5D submitted 2020-02-24 math.GT

Takefumi Nosaka This is my paper · ORCID
classification math.GT
keywords alexandergrouppolynomialsintroduceknottwistedclassclasses
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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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