Cohomology in algebra, geometry, physicsand statistics

Cyclic homology for bornological coarse spaces

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 homology 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].

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The online room    on ZOOM is open  at 11 AM for   a  virtual coffee.   At the same  time   the    blue  lecture  room on the ground  floor of the  rear building   on Zitna  25    shall be open  for  offline  meeting.

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