Equivariant cohomology of 2-group actions

• Grant number: 20/05524-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2020
• End date: November 30, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Cristián Andrés Ortiz González
• Grantee: Luis Alejandro Barbosa Torres
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project we study equivariant cohomology of Lie 2-groups acting on Lie groupoids. We investigate how the models of equivariant cohomology studied by Barbosa and Neumann (arXiv:1912.00316) extend to this setting. Our main goal is the study of equivariant cohomology of differentiable stacks with symmetries, hence we investigate the corresponding Morita invariance of the equivariant cohomology of a 2-group action. Finally, we expect to apply our theory to the study of characteristic classes of principal bundles over stacks by relating the equivariant cohomology of principal 2-group actions and the Chern-Weil homomorphism. (AU)