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Morita equivalences of vector bundles

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Matias del Hoyo
Universidade Federal Fluminense
Wed, 02/05/2018 - 10:30 - 12:00
MPIM Lecture Hall

VB-groupoids are vector bundles over Lie groupoids. They arise naturally, with the tangent and cotangent constructions as prominent examples, and admit a nice interpretation in terms of representations up to homotopy. In this talk, based on the work arXiv:1612.09289 joint with C. Ortiz, I will review these concepts and describe the behavior of vector bundles under Morita equivalences. I will explain how this leads to a convenient notion of 2-vector bundle over stacks, present some applications to Poisson geometry, and discuss further lines of research.

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