Noncommutative Geometry Seminar

Date: September 9, 2015

Time: 2:00PM - 3:00PM

Location: BLOC 628

Speaker: Branimir Ćaćić, Texas A&M University

Title: Good quotients of noncommutative Riemannian manifolds

Abstract: If the quotient of a compact Hausdorff space by a suitable group action is again a compact Hausdorff space, then the C*-algebra of the quotient is simply the fixed point subalgebra of the C*-algebra of the original space. If the quotient of a compact oriented Riemannian manifold by a suitable Lie group action is again a compact oriented Riemannian manifold, what happens at the level of spectral triples? In this talk, I will discuss an unbounded KK-theoretic construction of a good quotient for the spectral triple corresponding to a generalised Dirac operator equivariant under a free, orientation-preserving, and isometric smooth action of a compact connected Lie group. As time permits, I will then discuss applications to explicit unbounded KK-theoretic factorisations of noncommutative principal bundles arising via Rieffel's strict deformation quantisation. This is joint work with Bram Mesland.