Locally equivalent Floer complexes and unoriented link cobordisms

Cavallo, Alberto

doi:10.2140/agt.2024.24.3235

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Locally equivalent Floer complexes and unoriented link cobordisms

Alberto Cavallo

Algebraic & Geometric Topology 24 (2024) 3235–3290

DOI: 10.2140/agt.2024.24.3235

Abstract

We show that the local equivalence class of the collapsed link Floer complex $c C F L^{\infty} (L)$ , together with many $Υ$ –type invariants extracted from this group, is a concordance invariant of links. In particular, we define a version of the invariants $Υ_{L} (t)$ and $ν^{+} (L)$ when $L$ is a link and we prove that they give a lower bound for the slice genus $g_{4} (L)$ .

Furthermore, in the last section of the paper we study the homology group $H F L^{'} (L)$ and its behavior under unoriented cobordisms. We obtain that a normalized version of the $υ$ –set, introduced by Ozsváth, Stipsicz and Szabó, produces a lower bound for the $4$ –dimensional smooth crosscap number $γ_{4} (L)$ .

Keywords

link, concordance, slice genus, unoriented, link Floer homology

Mathematical Subject Classification

Primary: 57K10, 57K18

References

Publication

Received: 13 October 2020

Revised: 3 August 2022

Accepted: 1 December 2022

Published: 7 October 2024

Authors

Alberto Cavallo
Max Planck Institute for Mathematics Bonn Germany
https://sites.google.com/view/albertocavallomath

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Volume 24, issue 6 (2024)