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arXiv · 2111.05755

Quasi-representations of groups and two-homology

Marius Dadarlat
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Abstract

The Exel-Loring formula asserts that two topological invariants associated to a pair of almost commuting unitary matrices coincide. Such a pair can be viewed as a quasi-representation of $\mathbb{Z}^2$. We give a generalization of this formula for countable discrete groups. We also show the nontriviality of the corresponding invariants for quasidiagonal groups which are coarsely embeddable in a Hilbert space and have nonvanishing second Betti number.

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Marius Dadarlat. 2021-11-10. Quasi-representations of groups and two-homology. https://doi.org/10.1007/s00220-022-04373-2

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