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@article{faucris.268263891,
abstract = {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 Z_{2}-valued invariant. The first set of results provides index formulas expressing each of these 16 Z_{2}-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 Z_{2}-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 insulator},
author = {Doll, Nora and Schulz-Baldes, Hermann},
doi = {10.1016/j.aim.2021.108038},
faupublication = {yes},
journal = {Advances in Mathematics},
keywords = {Index theory; Spectral flow; Z2-invariant},
note = {CRIS-Team Scopus Importer:2021-10-22},
peerreviewed = {Yes},
title = {{Skew} localizer and {Z2}-flows for real index pairings},
volume = {392},
year = {2021}
}