The contractibility of a topological group $G$ is equivalent to the triviality of the join $G*G$ viewed as a principal $G$-bundle, and as known any compact group $G\neq 1$ is noncontractible. We have recently formulated a wider conjecture [Baum,D,Hajac; Banach Center Publ.2015], which generalizes also the classical Borsuk-Ulam theorem, that there is no $G$-equivariant map from $X*G$ to $X$, for any compact $X$ with a free action of $G$. This has been just proved [Chirivatsu,Passer; arXiv:1604.02173v2] which should provide a solution of a major open problem in geometric topology on actions of p-adic groups. I'll discuss some noncommutative analogues of the notion of join and of the contractibility of quantum groups and show in which sense $SU_q(2)$ is noncontractible.

## Are compact quantum groups noncontractible ?

Research Group:

Prof.

Ludwik Dabrovski

Institution:

SISSA

Location:

A-136

Schedule:

Friday, May 20, 2016 - 12:00

Abstract: