On contact surgery and knot Floer invariants

TL;DR

This paper explores the relationships between contact invariants in Heegaard Floer homology and Legendrian knot invariants, revealing conditions under which these invariants are non-zero after contact surgeries.

Contribution

It establishes new links between contact invariants and Legendrian knot invariants using sutured Floer homology and limit constructions.

Findings

Non-vanishing contact invariants imply non-zero Legendrian invariants after certain surgeries.

Uses sutured Floer homology and limit constructions to relate contact and Legendrian invariants.

Provides conditions for invariants to remain non-zero post-surgery.

Abstract

We establish some general relations between Heegaard Floer based contact invariants. In particular, we observe that if the contact invariant of large negative, respectively positive, contact surgeries along a Legendrian knot does not vanish, then the Legendrian invariant, respectively the Legendrian inverse limit invariant, of that knot is non-zero. We use sutured Floer homology, and the limit constructions due to Golla, and Etnyre, Vela-Vick and Zarev.