Geometry and Quantum Theory Seminar: Vasily Krylov (Harvard)

Following a paper of Calle and Liu we show that, under suitable tameness assumptions, the classifying space of the Morse category associated to a manifold M with a Morse function recovers the homotopy type of M, thereby addressing a gap in a preprint of Cohen-Jones-Segal. We also give a counterexample when those assumptions are not satisfied.