Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Jonathan Block; Varghese Mathai; 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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