Ozsvath-Szabo invariants and tight contact three-manifolds, II

Details Ozsvath-Szabo invariants and tight contact three-manifolds, II Ozsvath-Szabo invariants and tight contact three-manifolds, II

2004-04-06

arxiv.org/abs/math/0404136v4

Mathematics

Symplectic Geometry

35 pages, 10 figures, very small changes

Scientific paper

Let p and n be positive integers with p>1, and let E(p,n) be the oriented 3-manifold obtained by performing pn(p-1)-1 surgery on a positive torus knot of type (p, pn+1). We prove that E(2,n) does not carry tight contact structures for any n, while E(p,n) carries tight contact structures for any n and any odd p. In particular, we exhibit the first infinite family of closed, oriented, irreducible 3-manifolds which do not support tight contact structures. We obtain the nonexistence results via standard methods of contact topology, and the existence results by using a quite delicate computation of contact Ozsvath-Szabo invariants.

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