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Noncommutative Geometry Seminar

Wednesday, November 11, 2015
3:30pm to 4:30pm
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Good Quotients of Spectral Triples
Branimir Cacic, Visiting Assistant Professor, Mathematics, Texas A & M University,

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 what it means for a compact Lie group action on a spectral triple to admit a good quotient in the form of a spectral triple, and I will give an unbounded KK-theoretic construction of a good quotient for the commutative spectral triple corresponding to a generalised Dirac operator equivariant under a free and isometric action of a compact connected Lie group. As time permits, I will then discuss applications to noncommutative principal bundles arising via Rieffel's strict deformation quantisation. This is joint work with Bram Mesland.

For more information, please contact Farzad Fathizadeh by email at [email protected] or visit http://www.math.caltech.edu/~ncg/.