An algorithm to compare Legendrian knots

Abstract:

We have worked out a general method to decide whether two given Legendrian knots are Legendrian equivalent. The method yields a formal algorithmic solution to the problem (with very high algorithmic complexity) and, in certain circumstances, allows one to distinguish Legendrian knots practically, including some cases in which the computation of any known algebraic invariant except for the two classical ones (Thurston--Bennequin's and Maslov's) is infeasible. We use this, in particular, to provide an example of an annulus embedded in the three-sphere and tangent to the contact structure along the whole boundary, such that the two connected components of the boundary are not equivalent as Legendrian knots.

The talk is based on joint works with Maxim Prasolov and Vladimir Shastin.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( chat | slides )

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Geometry and topology online

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