Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T16:04:51.268Z Has data issue: false hasContentIssue false
  • English
  • Français

On the vanishing problem of string classes

Part of: Homotopy theory Differential topology

Published online by Cambridge University Press:  09 April 2009

Katsuhiko Kuribayashi
Katsuhiko Kuribayashi
Affiliation:
Department of Applied Mathematics Okayama University of Science1-1 Ridai-cho, Okayama 700Japan e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The ordinary string class is an obstruction to lift the structure group LSpin(n) of a loop group bundle LQ → LM to the universal central extension of LSpin(n) by the circle. The vanishing problem of the ordinary string class and generalized string classes are considered from the viewpoint of the ring structure of the cohomology H*(M; R).

MSC classification

Secondary: 57R20: Characteristic classes and numbers 55P35: Loop spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 2 , October 1996 , pp. 258 - 266
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Asada, A., Four lectures on geometry of loop group and non Abelian de Rham theory (Chalmers University of Technology/The University of Göteborg, 1990).Google Scholar
[2]Burghelea, D. and Vigué-Poirrier, M., Cyclic homology of commutative algebras I, Lecture Notes in Math. 1318 (Springer, Berlin, 1988), 51–72.Google Scholar
[3]Getzler, E., Jones, J. D. S. and Petrack, S., ‘Differential form on loop spaces and the cyclic bar complex’, Topology 30 (1991), 339–371.Google Scholar
[4]Killingback, T. P., ‘World sheet anomalies and loop geometry’, Nucl. Phys. B 288 (1987), 578–588.CrossRefGoogle Scholar
[5]McLaughlin, D. A., ‘Orientation and string structures on loop space’, Pacific J. Math. 155 (1992), 143–156.CrossRefGoogle Scholar
[6]Smith, L., ‘Homological algebra and the Eilenberg-Moore spectral sequence’, Trans. Amer. Math. Soc. 129 (1967), 58–93.Google Scholar
[7]Sullivan, D., ‘Infinitesimal computations in topology’, Inst. Hautes Érudes Sci. Publ. Math. (1978), 269–0331.Google Scholar