Event № 419
NOTE: The series continues to January 29th and February 5th.
In algebraic topology, the Borsuk-Ulam theorem and its extensions place restrictions on maps between compact spaces. Essential to this story is the antipodal action on the sphere, which sends each point x to -x, so equivariant maps are commonly called "odd". The original Borsuk-Ulam theorem then says that there is no odd map from a sphere of high dimension to a sphere of low dimension. This may be extended to more general compact spaces with free actions of finite groups by considering connectivity of a domain X and dimension of a codomain Y.
I will present my work on extending this theorem and similar results to C*-algebras, as motivated by the results and conjectures of other researchers (Yamashita, Taghavi, Baum-Dabrowski-Hajac). Along the way, we will see how this point of view may be used to improve topological results, and how the noncommutative setting differs from the commutative setting.