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Symmetric chain
complexes, twisted Blanchfield pairings and knot
concordance
Allison N Miller and Mark Powell |
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Algebraic & Geometric Topology 18 (2018) 3425–3476
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Abstract |
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We give a formula for the duality structure of the –manifold obtained by doing zero-framed surgery along a knot in the –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 –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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Keywords
twisted Blanchfield pairing, symmetric Poincaré chain
complex, knot concordance
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57N70
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References |
Publication
Received: 29 October 2017
Revised: 30 April 2018
Accepted: 22 June 2018
Published: 18 October 2018
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Authors |
| Allison N Miller | |
| Department of Mathematics University of Texas at Austin Austin, TX United States |
Department of Mathematics Rice University Houston, TX United States |
| https://sites.google.com/view/anmiller | |
| Mark Powell | |
| Department of Mathematical
Sciences Durham University Durham United Kingdom |
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| http://maths.dur.ac.uk/users/mark.a.powell/ | |
