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Using secondary Upsilon invariants to rule out stable equivalence of knot complexes

Samantha Allen

Algebraic & Geometric Topology 20 (2020) 29–48
Abstract

Two Heegaard Floer knot complexes are called stably equivalent if an acyclic complex can be added to each complex to make them filtered chain homotopy equivalent. Hom showed that if two knots are concordant, then their knot complexes are stably equivalent. Invariants of stable equivalence include the concordance invariants τ, 𝜀 and ϒ. Feller and Krcatovich gave a relationship between the Upsilon invariants of torus knots. We use secondary Upsilon invariants, defined by Kim and Livingston, to show that these relations do not extend to stable equivalence.

Keywords
stable equivalence, Upsilon, torus knot
Mathematical Subject Classification 2010
Primary: 57M25
References
Publication
Received: 10 July 2017
Accepted: 4 June 2019
Published: 23 February 2020
Authors
Samantha Allen
Department of Mathematics
Dartmouth College
Hanover, NH
United States