Detecting non-trivial elements in the spaces of Legendrian knots via Algebraic K-theory

This talk is based on a joint work with Thomas Kragh. Using the generating function theory we split inject homotopy groups of pseudo-isotopy and/or h-cobordism spaces into various spaces of Legendrian manifolds, e.g. the space of Legendrian unknots in ℝ2n+1 for a sufficiently large n. For instance, there is a non-trivial element in π2 of the space of Legendrian unknots in ℝ2n+1 for n≥12.