Heegaard Floer invariants of Legendrian knots in contact three--manifolds
arXiv:0802.0628
Abstract
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.
arXiv comment70 pages, 30 figures
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- Dehn Twists in Heegaard Floer Homology
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- On the equivalence of contact invariants in sutured Floer homology theories
- On the transverse invariant for bindings of open books
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- On loose Legendrian knots in rational homology spheres
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