Locally equivalent Floer complexes and unoriented link cobordisms

Abstract

We show that the local equivalence class of the collapsed link Floer complex $cCF{L}^{\infty }(L)$, together with many ${\rm Y}$-type invariants extracted from this group, is a concordance invariant of links. In particular, we define a version of the invariants ${{\rm Y}}_L(t)$ and ${\nu }^{+}(L)$ 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 $HF{L}^{\prime }(L)$ 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 ${\gamma }_4(L)$.

Corrected proofs. Accepted for publication in Algebr. Geom. Topol

References in corpus (7)

• Floer homology and knot complements
• Link cobordisms and functoriality in link Floer homology
• Connected sums and involutive knot Floer homology
• The concordance invariant tau in link grid homology
• On the Upsilon invariant and satellite knots
• Using secondary Upsilon invariants to rule out stable equivalence of knot complexes
• Upsilon type concordance invariants

Cited by in corpus (2)

• Fibered and strongly quasi-positive $L$-space links
• Slice-torus link invariants, combinatorial invariants, and positivity conditions