Capping off open books and the Ozsvath-Szabo contact invariant

Details Capping off open books and the Ozsvath-Szabo contact invariant Capping off open books and the Ozsvath-Szabo contact invariant

2009-01-24

arxiv.org/abs/0901.3797v4

Mathematics

Symplectic Geometry

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

Scientific paper

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.

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