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

Grant number: 10/08452-0
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): August 01, 2010
Effective date (End): January 31, 2013
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal researcher:Mauro Spreafico
Grantee:Fabio Ferrari Ruffino
Home 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.