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Algebras in Analysis
September 14, 2018 18:05–19:35, Moscow, Lomonosov Moscow State University, room 13-20.

Noncommutative fundamental group

P. R. Ivankov

Abstract: We define a fundamental group $\pi_1(A)$ on a class of $C^*$-algebras. The class of $C^*$-algebras on which the fundamental group is defined and is nontrivial includes
- Commutative $C^*$-algebras
- Continuous-trace $C^*$-algebras,
- The noncommutative torus,
- Isospectral deformations,
- Foliation $C^*$-algebras,
- The quantum SO(3) group.
We prove the following result.
If $X$ is a connected, locally path connected, semilocally simply connected, second countable, locally compact Hausdorff space, and if the fundamental group $\pi_1(X, x_0)$ is finitely approximable, then there is a group isomorphism $\pi_1(X, x_0)\cong\pi_1(C_0(X))$, which is unique up to an inner automorphism.
Some detalis are given in the following preprint:
http://www.mathframe.com/articles/noncommutative/noncommutative_geometry_of_quantized_coverings.pdf

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