A friendly introduction to the bordered contact invariant

Abstract

We give a short introduction to the contact invariant in bordered Floer homology defined by Földvári, 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.

Expanded the exposition, reorganized, and added new examples. 23 pages, 17 figures

References in corpus (6)

• Knot Floer homology detects fibred knots
• Contact structures, sutured Floer homology and TQFT
• Bordered Floer homology for sutured manifolds
• Joining and gluing sutured Floer homology
• Foliated Open Books
• Bordered Floer homology and contact structures