The triangulation conjecture
The triangulation conjecture

Ciprian Manolescu , UCLA
Fine Hall 314
The triangulation conjecture stated that any ndimensional topological manifold is homeomorphic to a simplicial complex. It is true in dimensions at most 3, but false in dimension 4 by the work of Casson and Freedman. In this talk I will explain the proof that the conjecture is also false in higher dimensions. This result is based on previous work of GalewskiStern and Matumoto, who reduced the problem to a question in low dimensions (the existence of elements of order 2 and Rokhlin invariant one in the 3dimensional homology cobordism group). The lowdimensional question can be answered in the negative using a variant of Floer homology, Pin(2)equivariant SeibergWitten Floer homology.