Doll N, Schulz-Baldes H (2021)
Publication Language: English
Publication Type: Journal article
Publication year: 2021
Book Volume: 392
Article Number: 108038
DOI: 10.1016/j.aim.2021.108038
Real index pairings of projections and unitaries on a separable Hilbert space with a real structure are defined when the projections and unitaries fulfill symmetry relations invoking the real structure, namely projections can be real, quaternionic, even or odd Lagrangian and unitaries can be real, quaternionic, symmetric or anti-symmetric. There are 64 such real index pairings of real K-theory with real K-homology. For 16 of them, the index of the Fredholm operator representing the pairing vanishes, but there is a secondary Z2-valued invariant. The first set of results provides index formulas expressing each of these 16 Z2-valued pairings as either an orientation flow or a half-spectral flow. The second and main set of results constructs the skew localizer for a pairing stemming from an unbounded Fredholm module and shows that the Z2-invariant can be computed as the sign of the Pfaffian of the skew localizer and in 8 of the cases as the sign of the determinant of the off-diagonal entry of the skew localize. This is of relevance for the numerical computation of invariants of topological insulators.
APA:
Doll, N., & Schulz-Baldes, H. (2021). Skew localizer and Z2-flows for real index pairings. Advances in Mathematics, 392. https://doi.org/10.1016/j.aim.2021.108038
MLA:
Doll, Nora, and Hermann Schulz-Baldes. "Skew localizer and Z2-flows for real index pairings." Advances in Mathematics 392 (2021).
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