

Algebras in Analysis
September 14, 2018 18:05–19:35, Moscow, Lomonosov Moscow State University, room 1320.






Noncommutative fundamental group
P. R. Ivankov^{} 
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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
 Continuoustrace $C^*$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

