Skip to main content

Representations up to homotopy and their cohomology

Posted in
Speaker: 
Cristián Ortiz
Affiliation: 
Universidade de São Paulo
Date: 
Wed, 2019-11-13 10:30 - 12:00
Location: 
MPIM Lecture Hall

Representations up to homotopy of Lie groupoids were introduced by Arias Abad and Crainic offering a conceptually clear setting to define the adjoint representation of a Lie groupoid. A representation up to homotopy (ruth) is defined as a certain differential graded module, so one can talk about the cohomology of a ruth. A result of Gracia Saz and Mehta says that any ruth on a 2-term graded vector bundle corresponds a geometric object called a VB-groupoid. In this seminar, we will show that the cohomology of a 2-term ruth of a Lie groupoid is a Morita invariant, hence yielding a cohomology of the associated differentiable stack. Then I will discuss how this extends to ruth’s on arbitrary graded bundles. The talk is based on a joint work with M. del Hoyo (Rio de Janeiro) and ongoing project with M. Del Hoyo (Rio de Janeiro) and Fernando Studzinski (Sao Paulo).

© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A