Cohomology of differentiable stacks via representations up to homotopy

• Grant number: 15/01698-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: July 01, 2015
• End date: May 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Cristián Andrés Ortiz González
• Grantee: Fernando Studzinski Carvalho
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

This projects aims at introducing cohomology theories of differentiable stacks via cohomologies associated to Lie groupoids. Concretely, we investigate the invariance under Morita equivalence of the cohomology of a Lie groupoid, with coefficients in a representation up to homotopy, hence giving rise to a cohomology theory of the stack associated to a Lie groupoid. Additionally, we also investigate the relation between representations up to homotopy and higher gauge theories. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

CARVALHO, Fernando Studzinski. On the cohomology of representations up to homotopy of Lie groupoids. 2019. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.