Abstract: I will discuss an invariant which can be defined for a large class of compact manifolds (conjecturally for all), which is a homotopy invariant for a large class of manifolds (conjecturally for all) and which, for odd dimensional hyperbolic manifolds, is the hyperbolic volume.
The description and the study of this invariant is an illustration for the use of the methods of linear algebra à la von Neumann (the linear algebra of G-Hilbert modules of finite type, with G the fundamental group of the manifold) and of its analytic version, the theory of pseudodifferential operators in bundles of G-Hilbert modules of finite type.
The work on L2-torsion involved many researchers beginning with Novikov- Shubin, Lott, Carey-Mathai, Farber, Lück-Rothenberg and others. The use of the methods of linear algebra à la Von Neumann in topology was pioneered by Atiyah-Singer, Novikov-Shubin, Cheeger-Gromov and in these days, is in the attention of many researchers. The invariants produced have often surprising geometric significance and look promising for topologists.
|Web page: Alexandru I. Suciu||Created: Feb. 2, 1999 Updated: Feb. 2, 1999|
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