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- Title
The KO-valued spectral flow for skew-adjoint Fredholm operators.
- Authors
Bourne, Chris; Carey, Alan L.; Lesch, Matthias; Rennie, Adam
- Abstract
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 / 2 ℤ -valued spectral flow in the study of topological phases of matter.
- Subjects
FREDHOLM operators; HILBERT space; PHASES of matter; SELFADJOINT operators; CLIFFORD algebras
- Publication
Journal of Topology & Analysis, 2022, Vol 14, Issue 2, p505
- ISSN
1793-5253
- Publication type
Article
- DOI
10.1142/S1793525320500557