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arXiv · 1911.03659

Locally equivalent Floer complexes and unoriented link cobordisms

Alberto Cavallo
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Abstract

We show that the local equivalence class of the collapsed link Floer complex $cCFL^\infty(L)$, 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 $HFL'(L)$ and its behaviour under unoriented cobordisms. We obtain that a normalized version of the $\upsilon$-set, introduced by Ozsváth, Stipsicz and Szabó, produces a lower bound for the 4-dimensional smooth crosscap number $γ_4(L)$.

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BibTeXRIS

Alberto Cavallo. 2023-06-13. Locally equivalent Floer complexes and unoriented link cobordisms. https://doi.org/10.2140/agt.2024.24.3235

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