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Are compact quantum groups noncontractible ?

Prof.
Ludwik Dabrovski
Institution: 
SISSA
Location: 
A-136
Schedule: 
Friday, May 20, 2016 - 12:00
Abstract: 

 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. 

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