Symmetric chain complexes, twisted Blanchfield pairings and knot concordance

Miller, A. N. and Powell, M. (2018) Symmetric chain complexes, twisted Blanchfield pairings and knot concordance. Algebraic and Geometric Topology, 18(6), pp. 3425-2476. (doi: 10.2140/agt.2018.18.3425)

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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.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Powell, Dr Mark
Authors: Miller, A. N., and Powell, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Algebraic and Geometric Topology
Publisher:Mathematical Sciences Publishers
ISSN (Online):1472-2739
Published Online:18 October 2018

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