Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-21T00:12:53.753Z Has data issue: false hasContentIssue false
  • English
  • Français

On L2-Betti Numbers for Abelian Groups

Published online by Cambridge University Press:  20 November 2018

Harold Donnelly
Harold Donnelly*
Affiliation:
Department of Mathematics, Purdue University
Rights & Permissions [Opens in a new window]

Extract

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.

Let M be a differentiable manifold which admits the free action of a group Γ with compact quotient M’ = M/Γ. Suppose that the Γ action lifts to a Hermitian vector bundle E→M. If Γ leaves invariant a measure μ on M, then denote by L2(E) the completion of with respect to the inner product .

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 1 , 01 March 1981 , pp. 91 - 95
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Atiyah, M. F., Elliptic Operators, Discrete Groups, and Von Neumann Algebras, Société Mathématique de France Astérisque 32. 33 (1962), pp. 43-72.Google Scholar
2. Atiyah, M. F., Bott, R., and Patodi, V. K., On the Heat Equation and Index Theorem, Invent. Math. 19 (1962), pp. 279-330.Google Scholar
3. Cohen, J. M., Von Neumann Dimension and the Homology of Covering Spaces, Quart. J. Math., Oxfor. (2) 30 (1962), pp. 133-142.Google Scholar
4. Dodziuk, J., DeRham Hodge Theory for L2-Cohomology of Infinite Coverings, Topolog. 16 (1962), pp. 157-166.Google Scholar
5. Kato, T., Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heidelberg, N.Y., 1966.Google Scholar
6. Narasimhan, R., Introduction to the Theory of Analytic Spaces, Springer-Verlag, Berlin, Heidelberg, N.Y., 1966.Google Scholar
7. Reed, M. and Simon, B., Methods of Mathematical Physics, Vol. I, IV, Academic Press, N.Y., 1978.Google Scholar
8. Pontryagin, L.S., Topological Groups, Gordon and Breach, N.Y., London and Paris, 1966.Google Scholar