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June 2022 Twisted Alexander Invariants of Knot Group Representations
Takefumi Nosaka
Tokyo J. Math. 45(1): 215-236 (June 2022). DOI: 10.3836/tjm/1502179346

Abstract

Given a homomorphism from a knot group to a fixed group, we introduce an element of a K1-group, which is a generalization of (twisted) Alexander polynomials. We compare the K1-class with other Alexander polynomials. In terms of semi-local rings, we compute the K1-classes of some knots and show their non-triviality. We also introduce metabelian Alexander polynomials.

Citation

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Takefumi Nosaka. "Twisted Alexander Invariants of Knot Group Representations." Tokyo J. Math. 45 (1) 215 - 236, June 2022. https://doi.org/10.3836/tjm/1502179346

Information

Received: 11 August 2020; Revised: 30 November 2020; Published: June 2022
First available in Project Euclid: 26 August 2021

Digital Object Identifier: 10.3836/tjm/1502179346

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

Keywords: Alexander polynomial , Dieudonné determinant , K1-group , knot , Novikov ring , semi-local ring

Rights: Copyright © 2022 Publication Committee for the Tokyo Journal of Mathematics

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Vol.45 • No. 1 • June 2022
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