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# 12 April 2022: Sophie Emma Mikkelsen, Syddansk Universitet, Odense.

Sophie Emma Mikkelsen.  Split extensions and KK-equivalences for quantum projective spaces.

This talk will take place in the blue seminar room, back building, Žitná 25, and on Zoom.

In this talk, I will present an explicit KK-equivalence between the noncommutative $C^*$-algebra of continuous functions on the Vaksman–Soibelman quantum complex projective space $C(\mathbb{C}P_q^n)$ and the commutative algebra $\mathbb{C}^{n+1}$. The KK-equivalence is constructed by finding an explicit splitting for the short exact sequence of $C^*$-algebras $\mathcal{K}\to C(\mathbb{C}P_q^n)\to C(\mathbb{C}P_q^{n-1})$. In the construction of the splitting it is crucial that $C(\mathbb{C}P_q^n)$ can be described as a graph $C^*$-algebra due to Hong and Szymański.

This talk is based on joint work with Francesca Arici.