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Twisted Blanchfield pairings and twisted signatures III: Applications

Part of: Topological manifolds

Published online by Cambridge University Press:  15 April 2024

Maciej Borodzik ,
Anthony Conway  and
Wojciech Politarczyk
Maciej Borodzik
Affiliation:
Institute of Mathematics, University of Warsaw, Warsaw, Poland
Anthony Conway*
Affiliation:
The University of Texas at Austin, Austin TX 78712, USA
Wojciech Politarczyk
Affiliation:
Institute of Mathematics, University of Warsaw, Warsaw, Poland
*
Corresponding author: Anthony Conway; Email: anthony.conway@austin.utexas.edu
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Abstract

This paper describes how to compute algorithmically certain twisted signature invariants of a knot $K$ using twisted Blanchfield forms. An illustration of the algorithm is implemented on $(2,q)$-torus knots. Additionally, using satellite formulas for these invariants, we also show how to obstruct the sliceness of certain iterated torus knots.

Keywords

Knot concordanceTwisted Blanchfield formsTwisted Alexander polynomials

MSC classification

Primary: 57N70: Cobordism and concordance
Type
Research Article
Information
Glasgow Mathematical Journal , First View , pp. 1 - 40
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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