Loring TA, Schulz-Baldes H (2020)
Publication Type: Journal article
Publication year: 2020
Book Volume: 14
Pages Range: 1-23
Journal Issue: 1
DOI: 10.4171/JNCG/357
Even index pairings are integer-valued homotopy invariants combining an even Fredholm module with a Ko-class specified by a projection. Numerous classical examples are known from differential and non-commutative geometry and physics. Here it is shown how to construct a finite-dimensional self-adjoint and invertible matrix, called the spectral localizer, such that half its signature is equal to the even index pairing. This makes the invariant numerically accessible. The index-theoretic proof heavily uses fuzzy spheres.
APA:
Loring, T.A., & Schulz-Baldes, H. (2020). The spectral localizer for even index pairings. Journal of Noncommutative Geometry, 14(1), 1-23. https://doi.org/10.4171/JNCG/357
MLA:
Loring, Terry A., and Hermann Schulz-Baldes. "The spectral localizer for even index pairings." Journal of Noncommutative Geometry 14.1 (2020): 1-23.
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