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

2008/07/22 by А. В. Ершов, A. V. Ershov, Ershov, A. V. · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #math.KT

paper · pdf · doi:10.48550/arxiv.0807.3544

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

arxiv created 2010/08/29 · arxiv updated 2010/08/31

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.

Citations

• Principal bundles with groupoid structure: local vs. global theory and nonabelian ucech cohomology

Cited by

• On K-theory automorphisms related to bundles of finite order
• On bundles related to groupoids of matrix subalgebras
• A model of the twisted K-theory related to bundles of finite order

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