Abstract
It is shown in this paper that the topological phenomenon“zero in the continuous spectrum”, discovered by S.P. Novikov and M.A. Shubin, can be explained in terms of a homology theory on the category of finite polyhedra with values in a certain abelian category. This approach implies homotopy invariance of the Novikov-Shubin invariants. Its main advantage is that it allows the use of the standard homological techniques, such as spectral sequences, derived functors, universal coefficients etc., while studying the Novikov-Shubin invariants. It also leads to some new quantitative invariants, measuring the Novikov-Shubin phenomenon in a different way, which are used in the present paper in order to strengthen the Morse type inequalities of Novikov and Shubin [NSh2].
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The research was supported by a grant from US-Israel Binational Science Foundation.
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Farber, M.S. Homological algebra of Novikov-Shubin invariants and morse inequalities. Geometric and Functional Analysis 6, 628–665 (1996). https://doi.org/10.1007/BF02247115
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DOI: https://doi.org/10.1007/BF02247115