Quasi-Representations of Groups and Two-Homology

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