Mathematics Colloquia and Seminars

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One of the interesting questions in Contact Geometry is the following: If one considers two Legendrian knots K and K' in the standard contact space (R^3 with alpha= ydx-dz), which are topologically equivalent and which have equal Thurston-Bennequin and Maslov numbers, are they Legendrian isotopic? In my talk I will show that the answer to this question is "not necessarily" by presenting the generalized version of an example suggested to us by Yasha Eliashberg. I will explain and use the new homology-type invariant for Legendrian knots, which was introduced by Chekanov and Eliashberg in independent works in 1997. Furthermore I will present an interesting result for transverse knots which was obtained through further studies of the above mentioned example.