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2020 Using secondary Upsilon invariants to rule out stable equivalence of knot complexes
Samantha Allen
Algebr. Geom. Topol. 20(1): 29-48 (2020). DOI: 10.2140/agt.2020.20.29

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.

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Samantha Allen. "Using secondary Upsilon invariants to rule out stable equivalence of knot complexes." Algebr. Geom. Topol. 20 (1) 29 - 48, 2020. https://doi.org/10.2140/agt.2020.20.29

Information

Received: 10 July 2017; Accepted: 4 June 2019; Published: 2020
First available in Project Euclid: 19 July 2021

Digital Object Identifier: 10.2140/agt.2020.20.29

Subjects:
Primary: 57M25

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 1 • 2020
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