Vector bundles over Lie groupoids and related structures
Matias del Hoyo (Universidade Federal Fluminense)
Abstract: The differentiation of a Lie groupoid yields a Lie algebroid and the transverse geometry of a Lie groupoid is encoded in a differentiable stack. These two constructions admit partial inverses, thus setting a bridge between the theories of algebroids and stacks, which has shown to be useful when dealing for instance with representations and cohomology. In this talk, I will overview vector bundles over Lie groupoids, Lie algebroids, and differentiable stacks, explain their key role in Poisson and Dirac geometries, discuss their behavior when crossing through that bridge, and mention some of my contributions to the subject.
mathematical physicsalgebraic geometrydifferential geometryrepresentation theorysymplectic geometry
Audience: researchers in the topic
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