Capping off open books and the Ozsvath-Szabo contact invariant

Abstract

If (S,h) is an open book with disconnected binding then we can form a new open book (S',h') by capping off one of the boundary components of S with a disk. We define a U-equivariant map on Heegaard Floer homology which sends c^+(S',h') to c^+(S,h), and we discuss various applications. In particular, we determine the support genera of almost all contact structures compatible with genus one, one boundary component open books. In addition, we compute the 3-dimensional invariant associated to any contact structure with non-vanishing contact invariant which is compatible with a genus one open book with periodic monodromy.

29 pages, 15 figures. Added section on support genera for genus one, one boundary component open books. Added result about gluing open books

References in corpus (5)

• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• A Legendrian surgery presentation of contact 3-manifolds
• Heegaard Floer homologies and contact structures
• On the contact class in Heegaard Floer homology
• Comultiplicativity of the Ozsvath-Szabo contact invariant

Cited by in corpus (1)

• Planar open books with four binding components