The KO-valued spectral flow for skew-adjoint Fredholm operators

18.06.2020, 16:15  –  Online-Seminar
Forschungsseminar Differentialgeometrie

Matthias Lesch (Bonn)

We give a comprehensive treatment of a ‘Clifford module flow’ along paths in the skew-adjoint Fredholm operators on a real Hilbert space that takes values in KO(R) via the Clifford index of Atiyah–Bott–Shapiro. We develop its properties for both bounded and unbounded skew-adjoint operators including an axiomatic characterization. Our constructions and approach are motivated by the principle that

spectral flow = Fredholm index.

That is, we show how KO–valued spectral flow relates to a KO–valued index by proving a Robbin–Salamon type result. The Kasparov product is also used to establish a spectral flow = Fredholm index result at the level of bivariant K-theory.

This is a report on joint work with Chris Bourne, Alan Carey, and Adam Rennie, completed at the University of Wollongong, Australia.

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