Legendrian contact homology in the product of a punctured Riemann surface and the real line

Details Legendrian contact homology in the product of a punctured Riemann surface and the real line Legendrian contact homology in the product of a punctured Riemann surface and the real line

2011-08-07

arxiv.org/abs/1108.1568v1

Mathematics

Symplectic Geometry

26 pages

Scientific paper

We give a combinatorial description of the Legendrian differential graded algebra associated to a Legendrian knot in PxR, where P is a punctured Riemann surface. As an application we show that for any integer k and any homology class h in H_1(PxR) there are k Legendrian knots all representing h which are pairwise smoothly isotopic through a formal Legendrian isotopy but which lie in mutually distinct Legendrian isotopy classes.

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