Geometry and Topology Seminar

  Manolescu has recently given a negative answer to the celebrated Triangulation conjecture (first stated by Kneser in 1924). His disproof  relies on the construction of a new invariant of spin rational homology three spheres obtained by studying the Seiberg-Witten equations from a  homotopy-theoretic point of view. In the present talk we discuss how to construct the analoguous invariants in the Morse-theoretic framework of  Kronheimer and Mrowka's monopole Floer homology. This approach works on every three manifold and is (somehow) functorial under cobordisms.