Mathematics > Geometric Topology
[Submitted on 24 Sep 2018 (v1), last revised 13 Jul 2022 (this version, v4)]
Title:Twisted Blanchfield pairings and twisted signatures II: Relation to Casson-Gordon invariants
View PDFAbstract:This paper studies twisted signature invariants and twisted linking forms, with a view towards obstructions to knot concordance. Given a knot $K$ and a representation $\rho$ of the knot group, we define a twisted signature function $\sigma_{K,\rho} \colon S^1 \to \mathbb{Z}$. This invariant satisfies many of the same algebraic properties as the classical Levine-Tristram signature $\sigma_K$. When the representation is abelian, $\sigma_{K,\rho}$ recovers $\sigma_K$, while for appropriate metabelian representations, $\sigma_{K,\rho}$ is closely related to the Casson-Gordon invariants. Additionally, we prove satellite formulas for $\sigma_{K,\rho}$ and for twisted Blanchfield forms.
Submission history
From: Anthony Conway [view email][v1] Mon, 24 Sep 2018 08:01:53 UTC (137 KB)
[v2] Sun, 13 Dec 2020 10:07:49 UTC (142 KB)
[v3] Sat, 20 Nov 2021 17:04:29 UTC (52 KB)
[v4] Wed, 13 Jul 2022 13:35:24 UTC (67 KB)
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