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arXiv · 1802.04517

The spectral localizer for even index pairings

Terry Loring·Hermann Schulz-Baldes
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Abstract

Even index pairings are integer-valued homotopy invariants combining an even Fredholm module with a $K_0$-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 selfadjoint 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.

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BibTeXRIS

Terry Loring, Hermann Schulz-Baldes. 2018-02-13. The spectral localizer for even index pairings. https://arxiv.org/abs/1802.04517

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