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Man Chuen Cheng
Wed 15 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133
The space of almost commuting tuples of unitary matrices
ESB 4133
Wed 15 Oct 2014, 3:15pm-4:15pm


Let G be a Lie group. The space Hom(Z^n,G) of commuting n-tuples in G was extensively studied over the last few years. Two related generalizations of this space are the space of almost commuting tuples, in the sense that the commutator of every pair of elements in each tuple is in the center of G, and the space of homomorphisms Hom(Gamma, G) from a central extension Gamma of a free abelian group by a free abelian group to G.

In this talk, I will describe the structures of these spaces and the relations between them in the case G=U(m). I will also discuss questions such as the number of path components and the rational homotopy type of these spaces.

This is joint work with Adem.