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Seminários do IMPA

Física Matemática

Simplicial vector bundles as Lie groupoid representations
Matias del Hoyo

Segunda-feira, 14 de outubro de 2019, 13:30
Sala 228

Lie groupoids are categorified manifolds; they provide a unified framework for classic geometries, and they can be used to model stacks in differential geometry. As Lie groups are represented by symmetries of a vector space, a convenient way to represent Lie groupoids, introduced by C. Abad and M. Crainic, is by symmetries of a graded vector bundle. I will present a new approach to the theory, developed jointly with G. Trentinaglia, by means of a semi-direct product construction, which sets a correspondence between simplicial vector bundles and Lie groupoid representations. As an application, I will mention a project developed jointly with C. Ortiz and F. Studzinski, on Morita invariance of Lie groupoid cohomology.