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2018 Symmetric chain complexes, twisted Blanchfield pairings and knot concordance
Allison N Miller, Mark Powell
Algebr. Geom. Topol. 18(6): 3425-3476 (2018). DOI: 10.2140/agt.2018.18.3425

Abstract

We give a formula for the duality structure of the 3–manifold obtained by doing zero-framed surgery along a knot in the 3–sphere, starting from a diagram of the knot. We then use this to give a combinatorial algorithm for computing the twisted Blanchfield pairing of such 3–manifolds. With the twisting defined by Casson–Gordon-style representations, we use our computation of the twisted Blanchfield pairing to show that some subtle satellites of genus two ribbon knots yield nonslice knots. The construction is subtle in the sense that, once based, the infection curve lies in the second derived subgroup of the knot group.

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Allison N Miller. Mark Powell. "Symmetric chain complexes, twisted Blanchfield pairings and knot concordance." Algebr. Geom. Topol. 18 (6) 3425 - 3476, 2018. https://doi.org/10.2140/agt.2018.18.3425

Information

Received: 29 October 2017; Revised: 30 April 2018; Accepted: 22 June 2018; Published: 2018
First available in Project Euclid: 27 October 2018

zbMATH: 06990069
MathSciNet: MR3868226
Digital Object Identifier: 10.2140/agt.2018.18.3425

Subjects:
Primary: 57M25, 57M27, 57N70

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 6 • 2018
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