Manolescu has recently given a negative answer to the celebrated Triangulation Conjecture. His disproof relies on the construction of a new invariant of rational homology three spheres equipped with a spin structure. This is obtained by studying the Seiberg-Witten equations from the point of view of Conley index theory. In the present talk we discuss how to construct the analogous invariants in the Morse-theoretic framework of Kronheimer and Mrowka's monopole Floer homology. This approach works on every three manifold and is functorial under cobordisms.