Topological obstructions to embedding of a matrix algebra bundle into a trivial one

Abstract

In the present paper we describe topological obstructions to embedding of a (complex) matrix algebra bundle into a trivial one under some additional arithmetic condition on their dimensions. We explain a relation between this problem and some principal bundles with structure groupoid. Finally, we briefly discuss a relation of our results to the twisted K-theory.

v.14: 29 pages, corrections and additions in Section 1

References in corpus (2)

• Principal bundles with groupoid structure: local vs. global theory and nonabelian ucech cohomology
• Theories of bundles with additional homotopy conditions

Cited by in corpus (4)

• A generalization of the topological Brauer group
• On bundles related to groupoids of matrix subalgebras
• A model of the twisted $K$-theory related to bundles of finite order
• On $K$-theory automorphisms related to bundles of finite order