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Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance

Miller, Allison N.; Powell, Mark

Authors

Allison N. Miller

Mark Powell



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.

Citation

Miller, A. N., & Powell, M. (2018). Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance. Algebraic & geometric topology, 18(6), 3425-3476. https://doi.org/10.2140/agt.2018.18.3425

Journal Article Type Article
Acceptance Date Jun 20, 2018
Online Publication Date Oct 18, 2018
Publication Date Oct 18, 2018
Deposit Date Mar 29, 2018
Publicly Available Date Mar 29, 2024
Journal Algebraic and Geometric Topology
Print ISSN 1472-2747
Electronic ISSN 1472-2739
Publisher Mathematical Sciences Publishers (MSP)
Peer Reviewed Peer Reviewed
Volume 18
Issue 6
Pages 3425-3476
DOI https://doi.org/10.2140/agt.2018.18.3425
Related Public URLs https://arxiv.org/abs/1709.08560

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