Homology, Homotopy and Applications

Volume 19 (2017)

Number 2

Twisted Blanchfield pairings and decompositions of 3-manifolds

Pages: 275 – 287

DOI: https://dx.doi.org/10.4310/HHA.2017.v19.n2.a14

Authors

Stefan Friedl (Fakultät für Mathematik, Universität Regensburg, Germany)

Constance Leidy (Department of Mathematics, Wesleyan University, Wesleyan Station, Middletown, Connecticut, U.S.A.)

Matthias Nagel (Département de Mathématiques, Université du Québec à Montréal, Canada)

Mark Powell (Département de Mathématiques, Université du Québec à Montréal, Canada)

Abstract

We prove a decomposition formula for twisted Blanchfield pairings of 3-manifolds. As an application we show that the twisted Blanchfield pairing of a 3-manifold obtained from a 3-manifold $Y$ with a representation $\phi : \mathbb{Z} [ \pi_1 (Y ) ] \to R$, infected by a knot $J$ along a curve $\eta$ with $\phi (\eta) \neq 1$, splits orthogonally as the sum of the twisted Blanchfield pairing of $Y$ and the ordinary Blanchfield pairing of the knot $J$, with the latter tensored up from $\mathbb{Z} [ t, t^{-1} ]$ to $R$.

Keywords

twisted Blanchfield pairing, infection by a knot

2010 Mathematics Subject Classification

57M25, 57M27, 57N70

Received 8 January 2017

Received revised 21 March 2017

Published 22 November 2017