Differential geometric invariants for time-reversal symmetric Bloch bundles, II : The low-dimensional “quaternionic” case

De Nittis, Giuseppe; Gomi, Kiyonori

doi:10.2140/agt.2023.23.2925

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Differential geometric invariants for time-reversal symmetric Bloch bundles, II: The low-dimensional “quaternionic” case

Giuseppe De Nittis and Kiyonori Gomi

Algebraic & Geometric Topology 23 (2023) 2925–2974

DOI: 10.2140/agt.2023.23.2925

Abstract

This paper is devoted to the construction of differential geometric invariants for the classification of “quaternionic” vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution that leaves fixed only a finite number of points, it is possible to prove that the Wess–Zumino term and the Chern–Simons invariant yield topological invariants able to distinguish between inequivalent realizations of “quaternionic” structures. This is a nontrivial generalization of results previously known only in the case of tori with time-reversal involution.

Keywords

topological quantum systems, “quaternionic” vector bundles, Wess–Zumino term, Chern–Simons invariant

Mathematical Subject Classification 2010

Primary: 57R22

Secondary: 53A55, 53C80, 55N25

References

Publication

Received: 23 October 2018

Revised: 2 March 2022

Accepted: 28 March 2022

Published: 26 September 2023

Authors

Giuseppe De Nittis
Facultad de Matemáticas & Instituto de Física Pontificia Universidad Católica de Chile Santiago Chile

Kiyonori Gomi
Department of Mathematics Tokyo Institute of Technology Tokyo Japan

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Volume 23, issue 7 (2023)