Using h-Cobordisms to Detect Non-Trivial Homotopy Groups in Spaces of Legendrian

Explore a mathematical lecture from the Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar where Uppsala University's Thomas Kragh delves into the detection of non-trivial homotopy groups in spaces of Legendrian through h-cobordisms. Learn about the space of h-cobordisms associated with manifold M, examining their non-trivial homotopy groups and computation methods using Waldhausen's algebraic K-theory of spaces. Discover the mapping between these spaces and specific spaces of Legendrians, with particular focus on detecting non-trivial behavior in homotopy groups. Examine a notable case study involving two copies of the h-cobordism space of a point within the space of Legendrians of the jet 1 bundle of the n-sphere, based at a standard Legendrian unknot (the Whitney sphere).