Twisted Blanchfield pairings and twisted signatures II: Relation to Casson-Gordon invariants

2018/09/24 by Borodzik, Maciej, Conway, Anthony, Politarczyk, Wojciech · 1 citation
#57K10 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1809.08791

Abstract

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 ρ of the knot group, we define a twisted signature function σ_K,ρ \colon S¹ → ℤ. This invariant satisfies many of the same algebraic properties as the classical Levine-Tristram signature σ_K. When the representation is abelian, σ_K,ρ recovers σ_K, while for appropriate metabelian representations, σ_K,ρ is closely related to the Casson-Gordon invariants. Additionally, we prove satellite formulas for σ_K,ρ and for twisted Blanchfield forms.

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