Non-integral bundles and gerbes; twisted K-theory and cohomology.

• Grant number: 10/08452-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2010
• End date: January 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Mauro Spreafico
• Grantee: Fabio Ferrari Ruffino
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

We study the geometry of "non-integral" bundles and gerbes with connection. Such objects naturally arise as trivializations of flat gerbes in the abelian case, and we try to investigate, at least for vector bundles, the non-abelian generalization. We then discuss the relations between differential cohomology classes and non-integral gerbes, and the relations between non-integral bundles and twisted bundles.