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.
Original language | English (US) |
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Pages (from-to) | 1307-1363 |
Number of pages | 57 |
Journal | Journal of the European Mathematical Society |
Volume | 11 |
Issue number | 6 |
DOIs | |
State | Published - 2009 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics
Keywords
- Heegaard Floer homology
- Legendrian knots
- Transverse knots