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Cohomology in algebra, geometry, physicsand statistics
Cyclic homology for bornological coarse spaces CANCELLED because of COVID-19
Speaker’s name:
Luigi Caputi
Speaker’s affiliation:
Institute of Informatics of the Czech Academy of Sciences, Praha
Place:
in konirna seminar room of the front IM building, ground floor
Date:
Wednesday, 25. March 2020 - 11:30 to 12:30
Abstract:
Bornological coarse spaces are "large scale" generalizations of metric spaces (up to quasi-isometry). Homological invariants of such spaces are given by coarse homology theories, which are functors from the category of bornological coarse spaces to a stable cocomplete ∞-category, satisfying additional axioms. Among the main examples of coarse homology theories, there are coarse versions of ordinary homology, of topological
and algebraic K-theory. In the talk we define G-equivariant coarse versions of the classical Hochschild and cyclic homologies of algebras. If k is a field, the evaluation at the one point space induces equivalences with the classical Hochschild and cyclic homologies of k. In the equivariant setting, the G-equivariant coarse Hochschild (cyclic) homology of the discrete group G agrees with the classical Hochschild (cyclic) homology of the associated group algebra k[G].
and algebraic K-theory. In the talk we define G-equivariant coarse versions of the classical Hochschild and cyclic homologies of algebras. If k is a field, the evaluation at the one point space induces equivalences with the classical Hochschild and cyclic homologies of k. In the equivariant setting, the G-equivariant coarse Hochschild (cyclic) homology of the discrete group G agrees with the classical Hochschild (cyclic) homology of the associated group algebra k[G].