Homotopy invariance of Novikov-Shubin invariants and $L^2$ Betti numbers
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- by Jonathan Block, Varghese Mathai and Shmuel Weinberger PDF
- Proc. Amer. Math. Soc. 125 (1997), 3757-3762 Request permission
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.References
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Additional Information
- Jonathan Block
- Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania
- Email: blockj@math.upenn.edu
- Varghese Mathai
- Affiliation: Department of Pure Mathematics, University of Adelaide, Adelaide 5005, Australia
- MR Author ID: 231404
- Email: vmathai@maths.adelaide.edu.au
- Shmuel Weinberger
- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- MR Author ID: 181430
- Email: shmuel@math.uchicago.edu
- Received by editor(s): July 30, 1996
- Communicated by: Peter Li
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 3757-3762
- MSC (1991): Primary 58G11, 58G18, 58G25
- DOI: https://doi.org/10.1090/S0002-9939-97-04154-3
- MathSciNet review: 1425112