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Geometry-Topology Seminar

Thursday, December 10, 2020 - 4:30pm

Ivan Contreras Palacios

Amherst College


University of Pennsylvania

via Zoom

The Zoom link is: This same Zoom link will apply for future talks as well. It is set to open at 4 PM so that speakers can come on early and check out their technology setups. The talks will begin at 4:30 PM. We will also stay afterwards, say from 5:30 - 6 PM to chat with one another, as an online substitute for going out to dinner with our speakers. We encourage everyone to have a nice bottle of wine at hand for that social half hour. For further information about the seminar, please contact Mona Merling (, Davi Maximo ( or Herman Gluck (

Abstract: The genus integration of a Lie algebroid was introduced in joint work with Rui Fernandes as the quotient space of A-paths  by  A-homologies.  We prove that such integration is the abelianization of the Weinstein groupoid, and we also show that the obstructions to smoothness of the genus integration are controlled by the extended monodromy groups. In this talk we will survey the integration problem of Lie algebroids and these new results, and we will present an ongoing work on the particular case of the prequantization Lie algebroid associated with a closed 2-form. In particular our results recover the  prequantization condition as well as the usual description of principal circle bundles with connection via differential characters. Based on  joint work with Rui Fernandes.