NCG Seminar

[Emanuele Tuillier Illingworth]

*"NON-COMMUTATIVE GEOMETRY" SEMINAR 
<https://www.math.sissa.it/content/non-commutative-geometry-seminars>*

Friday 20 May 2016 at 12:00
Venue: SISSA, Room 136

Prof. Ludwik Dabrowski (SISSA)
"Are compact quantum groups noncontractible?"

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.