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Bundle gerbes for topological insulators. (English) Zbl 1397.53044
Carqueville, Nils (ed.) et al., Advanced school on topological quantum field theory. Selected papers based on the presentations at the advanced school, University of Warsaw, Warsaw, Poland, December 7–9, 2015. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-38-6/pbk). Banach Center Publications 114, 145-180 (2018).
Summary: Bundle gerbes are simple examples of higher geometric structures that show their utility in dealing with topological subtleties of physical theories. I will review a recent construction of torsion topological invariants for condensed-matter systems via equivariant bundle gerbes. The construction covers static and periodically driven systems with time reversal invariance in 2 and 3 space dimensions. It involves refinements of geometry of gerbes that will be discussed in the first lecture, the second one being devoted to the applications to topological insulators.
For the entire collection see [Zbl 1398.81009].

MSC:
53C08 Differential geometric aspects of gerbes and differential characters
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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