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June 19, 2014
Thursday, June 19
Noncommutative Geometry
Time: 13:00
Speaker: Branimir Cacic (Texas A&M)
Title: "A reconstruction theorem for noncommutative G-manifolds"
Room: MC 106

Abstract: Just as one can construct the noncommutative 2-torus as the strict deformation quantisation of the commutative 2-torus along the translation action, so too can one more generally construct noncommutative G-manifolds, namely, strict deformation quantisations of commutative spectral triples along the action of a compact abelian Lie group G. I will propose an abstract definition of noncommutative G-manifold, analogous to the definition of commutative spectral triple, and show that the deformation of an abstract noncommutative G-manifold with deformation parameter θH2(ˆG,T) by a class θH2(ˆG,T) yields an abstract noncommutative G-manifold with deformation parameter θ+θ; combined with Connes's reconstruction theorem for commutative spectral triples, this yields the analogue of Connes's reconstruction theorem for noncommutative G-manifolds. If time permits, I will also discuss a Pontrjagin-dual version of the Connes--Dubois-Violette splitting homomorphism and use it to show that sufficiently well-behaved rational noncommutative TN-manifolds are, in fact, almost-commutative.