Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
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

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.

topological quantum systems, “quaternionic” vector bundles, Wess–Zumino term, Chern–Simons invariant
Mathematical Subject Classification 2010
Primary: 57R22
Secondary: 53A55, 53C80, 55N25
Received: 23 October 2018
Revised: 2 March 2022
Accepted: 28 March 2022
Published: 26 September 2023
Giuseppe De Nittis
Facultad de Matemáticas & Instituto de Física
Pontificia Universidad Católica de Chile
Kiyonori Gomi
Department of Mathematics
Tokyo Institute of Technology

Open Access made possible by participating institutions via Subscribe to Open.