Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T23:16:37.486Z Has data issue: false hasContentIssue false
  • English
  • Français

A generalization of the topological Brauer group

Published online by Cambridge University Press:  04 March 2008

A. V. Ershov
A. V. Ershov
Affiliation:
ershov@higeom.math.msu.suDepartment of Mathematics, Moscow State University, Moscow, Russia
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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