Homotopy theory of bundles with fiber matrix algebra

Abstract

In the present paper we consider a special class of locally trivial bundles with fiber a matrix algebra. On the set of such bundles over a finite $CW$-complex we define a relevant equivalence relation. The obtained stable theory gives us a geometric description of the H-space structure $\BSU_\otimes$ on $\BSU$ related to the tensor product of virtual $\SU$-bundles of virtual dimension 1.

This is a version of the paper published as a preprint of Max Planck Institute for Mathematics. Several misprints are corrected. 24 pages

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