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Homotopy invariance of Novikov-Shubin invariants and |
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| Authors: | Jonathan Block Varghese Mathai Shmuel Weinberger |
| Institution: | Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania ; Department of Pure Mathematics, University of Adelaide, Adelaide 5005, Australia ; Department of Mathematics, University of Chicago, Chicago, Illinois 60637 |
| 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  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. |
| Keywords: | $L^2$ Betti numbers Novikov-Shubin invariants homotopy invariance von Neumann algebras |
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