Heegaard Floer invariants of Legendrian knots in contact three--manifolds

Details Heegaard Floer invariants of Legendrian knots in contact three--manifolds Heegaard Floer invariants of Legendrian knots in contact three--manifolds

2008-02-05

arxiv.org/abs/0802.0628v2

Mathematics

Symplectic Geometry

70 pages, 30 figures

Scientific paper

We define invariants of null--homologous Legendrian and transverse knots in contact 3--manifolds. The invariants are determined by elements of the knot Floer homology of the underlying smooth knot. We compute these invariants, and show that they do not vanish for certain non--loose knots in overtwisted 3--spheres. Moreover, we apply the invariants to find transversely non--simple knot types in many overtwisted contact 3--manifolds.

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