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 BorsukUlam 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 padic 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.
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Are compact quantum groups noncontractible ?
Research Group:
Prof.
Ludwik Dabrovski
Institution:
SISSA
Location:
A136
Schedule:
Friday, May 20, 2016  12:00
Abstract:
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