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Operator Algebra and Noncommutative Geometry Seminar Series

July 11, 2019 @ 3:30 pm - 4:30 pm


Asst Prof Chris Bourne (Tohoku University​) will be giving a talk​.


The Cayley transform and K-theory


The Cayley transform is a way to pass between unitary operators and self-adjoint (generally unbounded) operators on a Hilbert space or C*-module. I will review this construction and its application to an isomorphism between K-theory and Kasparov modules. Time permitting, I will also introduce a Z_2-graded analogue of this transform and its application to van Daele K-theory for graded C*-algebras. Explicit isomorphisms for all 8 real K-theory groups are a special case of this map. This is joint work with Johannes Kellendonk and Adam Rennie.


Building 39C Room 174, University of Wollongong
Wollongong, New South Wales 2522 Australia
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