Speaker: 

Ciprian Manolescu

Institution: 

UCLA

Time: 

Thursday, March 6, 2014 - 4:00pm

Host: 

Location: 

RH306

The triangulation conjecture stated that any n-dimensional
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 Galewski-Stern 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 3-dimensional homology
cobordism group). The low-dimensional question can be answered in the
negative using a variant of Floer homology, Pin(2)-equivariant
Seiberg-Witten Floer homology.