A friendly introduction to the bordered contact invariant

TL;DR

This paper introduces the bordered contact invariant in Floer homology, explaining its construction via foliated open books and demonstrating its vanishing for overtwisted structures through explicit computations.

Contribution

It provides a clear introduction to the bordered contact invariant, including a new procedure for constructing foliated open books and a local proof of vanishing for overtwisted contact structures.

Findings

Explicit computation showing vanishing of the invariant for overtwisted structures

Procedure for constructing foliated open books

Clarification of the contact invariant's properties in bordered Floer homology

Abstract

We give a short introduction to the contact invariant in bordered Floer homology defined by F\"oldv\'ari, Hendricks, and the authors. The construction relies on a special class of foliated open books. We discuss a procedure to obtain such a foliated open book and present a definition of the contact invariant. We also provide a "local proof", through an explicit bordered computation, of the vanishing of the contact invariant for overtwisted structures.