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A generalization of the topological Brauer group

Published online by Cambridge University Press:  04 March 2008

A. V. Ershov
A. V. Ershov
Affiliation:
[email protected] of Mathematics, Moscow State University, Moscow, Russia
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Abstract

In the present paper we study some homotopy invariants which can be defined by means of bundles with fiber being a matrix algebra. In particular, we introduce some generalization of the Brauer group in the topological context and show that any of its elements can be represented as a locally trivial bundle with the structure group , k ∈ . Finally, we discuss its possible applications in the twisted K-theory.

Keywords

matrix algebra bundleBrauer grouphomotopy functorfirst obstructiontwisted K-theoryoperator algebraFredholm operators
Type
Research Article
Information
Journal of K-Theory , Volume 2 , Special Issue 3: In Memory of Yurii Petrovich Solovyev October 8, 1944–September 11, 2003 , December 2008 , pp. 407 - 444
Copyright
Copyright © ISOPP 2008

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References

1.Adams, J. F.: Infinite Loop Spaces. Princeton, New Jersey, 1978CrossRefGoogle Scholar
2.Atiyah, M., Segal, G.: Twisted K-theory. arXiv preprint, math.KT/0407054Google Scholar
3.Ershov, A.V.: Homotopy theory of bundles with fiber matrix algebra. J. Math. Sci. (New York) 123, No.4 (2004), 4198–4220CrossRefGoogle Scholar
4.Ershov, A.V.: Formal group laws over Hopf algebras and their application to complex cobordism theory. Preprint 39 (2002), Max-Planck-Institut für MathematikGoogle Scholar
5.Ershov, A.V.: Symmetries in complex cobordism theory related to stable equivalence classes of SU-bundles. Preprint 70 (2002), Max-Planck-Institut für MathematikGoogle Scholar
6.Griffiths, Ph.A., Morgan, J. W.: Rational Homotopy Theory and Differential Forms. Birkhäuser, 1981Google Scholar
7.Grothendieck, A.: Le groupe de Brauer I. Sem. Bourbaki 290 (1964/1965), 21pGoogle Scholar
8.Mathai, V., Melrose, R. B., Singer, I.M.: The index of projective families of elliptic operators. Geometry & Topology 9 (2005), 341–373CrossRefGoogle Scholar
9.Palais, R.S.: On the homotopy of certain groups of operators. Topology 3 (1965), 271–279CrossRefGoogle Scholar
10.Pierce, R.S.: Associative Algebras. Springer Verlag, 1982CrossRefGoogle Scholar
11.Segal, G.B.: Categories and cohomology theories. Topology 13 (1974), 293–312CrossRefGoogle Scholar
12.Sullivan, D.: Geometric Topology: Localization, Periodicity and Galois Symmetry. K-Monographs in Mathematics 8, Springer, 2005Google Scholar