Seminar: Covering spaces and fundamental groupoids of noncommutative spaces
Clarisson Canlubo will give a talk on Covering spaces and fundamental groupoids of noncommutative spaces.
Abstract: Noncommutative geometry, a relatively new area of mathematics, at the moment has only K-theory and cyclic homology as sources of geometric invariants. In this talk we propose notions generalizing covering spaces and fundamental groupoids for noncommutative spaces. We will argue that certain comodule-algebras serve as covering spaces and a certain associated Hopf algebroid serves as the fundamental groupoid. We will give ample amount of examples: coverings of commutative spaces, coverings of noncommutative tori, coverings arising from deformation quantization, coverings of graphs and graph C*-algebras, and the Jones tower.
The lecture is part of the ALG/NCG/TOP Ph.D. students' seminar.