Abstract

We give a combinatorial description of the Legendrian differential graded algebra associated to a Legendrian knot in $$P\times {\mathbb R}$$, where $$P$$ is a punctured Riemann surface. As an application we show that, for any integer $$k$$ and any homology class $$h\in H_1(P\times {\mathbb R})$$, 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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