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Homotopy invariance of Novikov-Shubin invariants and $L^2$ Betti numbers

Authors: Jonathan Block, Varghese Mathai and Shmuel Weinberger
Journal: Proc. Amer. Math. Soc. 125 (1997), 3757-3762
MSC (1991): Primary 58G11, 58G18, 58G25.
MathSciNet review: 1425112
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Abstract: We give short proofs of the Gromov-Shubin theorem on the homotopy invariance of the Novikov-Shubin invariants and of the Dodziuk theorem on the homotopy invariance of the $L^2$ Betti numbers of the universal covering of a closed manifold in this paper. We show that the homotopy invariance of these invariants is no more difficult to prove than the homotopy invariance of ordinary homology theory.

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Additional Information

Jonathan Block
Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania

Varghese Mathai
Affiliation: Department of Pure Mathematics, University of Adelaide, Adelaide 5005, Australia

Shmuel Weinberger
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637

Keywords: $L^2$ Betti numbers, Novikov-Shubin invariants, homotopy invariance, von Neumann algebras.
Received by editor(s): July 30, 1996
Communicated by: Peter Li
Article copyright: © Copyright 1997 American Mathematical Society