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

2011/08/31 by Johan Björklund · 1 citation
Mathematics · #math.SG #math.GT

paper · pdf · doi:10.1112/jlms/jdw066

30 pages Clarified some arguments, corrected typos etc, corrected some minor errors

arxiv created 2015/06/03 · arxiv updated 2017/05/17

Abstract

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 H₁(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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