Geodesic
Differential geometric invariants for time-reversal symmetric Bloch bundles, II : The low-dimensional “quaternionic” case
De Nittis, Giuseppe1 ; Gomi, Kiyonori2
1 Facultad de Matemáticas & Instituto de Física, Pontificia Universidad Católica de Chile, Santiago, Chile
2 Department of Mathematics, Tokyo Institute of Technology, Tokyo, Japan
Algebraic and Geometric Topology, Tome 23 (2023) no. 7, pp. 2925-2974

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2023.23.2925
Classification : 57R22, 53A55, 53C80, 55N25
Keywords: topological quantum systems, “quaternionic” vector bundles, Wess–Zumino term, Chern–Simons invariant

De Nittis, Giuseppe 1 ; Gomi, Kiyonori 2

1 Facultad de Matemáticas & Instituto de Física, Pontificia Universidad Católica de Chile, Santiago, Chile
2 Department of Mathematics, Tokyo Institute of Technology, Tokyo, Japan 
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De Nittis, Giuseppe; Gomi, Kiyonori. Differential geometric invariants for time-reversal symmetric Bloch bundles, II : The low-dimensional “quaternionic” case. Algebraic and Geometric Topology, Tome 23 (2023) no. 7, pp. 2925-2974. doi: 10.2140/agt.2023.23.2925

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