Commutator estimates and Fredholm modules on sub-Riemannian manifolds

Heiko Gimperlein (Heriot-Watt University and Maxwell Institute)

Tuesday 27th May, 2014 16:00-17:00 Maths 416


In noncommutative geometry, operator norm estimates for commutators of first-order operators with non-smooth functions are vital to understand the Lipschitz algebra and the Connes metric associated with a spectral triple. This talk is going to discuss a Calderon commutator estimate on the Heisenberg group for the commutator of a pseudodifferential operator with a Hölder continuous function.
Translating between bounded and unbounded Fredholm modules, we conclude sharp weak Schatten-class estimates for commutators and operators of Hankel-type. Ideas of Connes then yield an analytic index-like formula for the mapping degree of a nonsmooth function, and we discuss applications to spectral triples on sub-Riemannian manifolds. (joint with M. Goffeng)

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