Title

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

RIS ID

146527

Publication Details

Bourne, C., Carey, A., Lesch, M. & Rennie, A. (2020). The KO-valued spectral flow for skew-adjoint Fredholm operators. Journal of Topology and Analysis, 1-52.

Abstract

© 2020 World Scientific Publishing Co. Pte Ltd. All rights reserved. In this paper, 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 the 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. We explain how our results incorporate previous applications of Z/2Z-valued spectral flow in the study of topological phases of matter.

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Link to publisher version (DOI)

http://dx.doi.org/10.1142/S1793525320500557