Gysin sequences and SU(2) ‐symmetries of C∗ ‐algebras

Motivated by the study of symmetries of C∗ ‐algebras, as well as by multivariate operator theory, we introduce the notion of an SU(2) ‐equivariant subproduct system of Hilbert spaces. We analyse the resulting Toeplitz and Cuntz–Pimsner algebras and provide results about their topological invariants through Kasparov's bivariant K ‐theory. In particular, starting from an irreducible representation of SU(2) , we show that the corresponding Toeplitz algebra is equivariantly KK ‐equivalent to the algebra of complex numbers. In this way, we obtain a six‐term exact sequence of K ‐groups containing a noncommutative analogue of the Euler class.