Parity as Z2-valued spectral flow

Doll N, Schulz-Baldes H, Waterstraat N (2019)

Publication Type: Journal article

Publication year: 2019

Journal

Bulletin of the London Mathematical Society London Mathematical Society

Book Volume: 51

Pages Range: 836-852

Journal Issue: 5

DOI: 10.1112/blms.12282

Abstract

This note is about the topology of the path space of linear Fredholm operators on a real Hilbert space. Fitzpatrick and Pejsachowicz introduced the parity of such a path, based on the Leray-Schauder degree of a path of parametrices. Here an alternative analytic approach is presented which reduces the parity to the Z2-valued spectral flow of an associated path of chiral skew-adjoints. Furthermore, the related notion of Z2-index of a Fredholm pair of chiral complex structures is introduced and connected to the parity of a suitable path. Several non-trivial examples are provided. One of them concerns topological insulators, another an application to the bifurcation of a non-linear partial differential equation.

Authors with CRIS profile

Nora Doll Lehrstuhl für Mathematik (Mathematische Physik) Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik)

Involved external institutions

Martin-Luther-Universität Halle-Wittenberg (MLU) DE Germany (DE)

How to cite

APA:

Doll, N., Schulz-Baldes, H., & Waterstraat, N. (2019). Parity as Z2-valued spectral flow. Bulletin of the London Mathematical Society, 51(5), 836-852. https://dx.doi.org/10.1112/blms.12282

MLA:

Doll, Nora, Hermann Schulz-Baldes, and Nils Waterstraat. "Parity as Z2-valued spectral flow." Bulletin of the London Mathematical Society 51.5 (2019): 836-852.

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