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2021 Twisted Alexander Invariants of Knot Group Representations
NOSAKA Takefumi
Tokyo J. Math. Advance Publication 1-22 (2021). DOI: 10.3836/tjm/1502179346

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 the $K_1$-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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NOSAKA Takefumi. "Twisted Alexander Invariants of Knot Group Representations." Tokyo J. Math. Advance Publication 1 - 22, 2021. https://doi.org/10.3836/tjm/1502179346

Information

Published: 2021
First available in Project Euclid: 26 August 2021

Digital Object Identifier: 10.3836/tjm/1502179346

Subjects:
Primary: 57M25
Secondary: 19B28, 57M27

Rights: Copyright © 2021 Publication Committee for the Tokyo Journal of Mathematics

JOURNAL ARTICLE
22 PAGES

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