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Explore a comprehensive lecture on the group cohomology and topological K-theory of groups $\Gamma=\mathbb{Z}^n\rtimes \Z/m$ with $m$ free of squares. Delve into the explicit computations of group cohomology for $\Gamma$ and associated toroidal orbifolds. Learn about the unique decomposition of $\mathbb{Z}/m$-lattices and the application of the Lyndon-Hoschild-Serre spectral sequence. Discover how the Baum-Connes conjecture is used to prove that the topological K-theory of the reduced group C*-algebra of $\Gamma$ is torsion free. Gain insights into the generalization of results by Adem-Gomez-Pan-Petrosyan and Davis-Luck-Langer in this joint work presented by Mario Velasquez from Universidad Nacional de Colombia and Luis Jorge Sánchez.
