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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
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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