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Novikov–Shubin invariant

From Wikipedia, the free encyclopedia

In mathematics, a Novikov–Shubin invariant, introduced by Sergei Novikov and Mikhail Shubin (1986), is an invariant of a compact Riemannian manifold related to the spectrum of the Laplace operator acting on square-integrable differential forms on its universal cover.

The Novikov–Shubin invariant gives a measure of the density of eigenvalues around zero. It can be computed from a triangulation of the manifold, and it is a homotopy invariant. In particular, it does not depend on the chosen Riemannian metric on the manifold.[1]

Notes

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  1. ^ Lück 2002, p. 104, Theorem 2.67.

References

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  • Cheeger, Jeff; Gromov, Mikhail (1985), "On the characteristic numbers of complete manifolds of bounded curvature and finite volume", in Chavel, Isaac; Farkas, Hershel M. (eds.), Differential geometry and complex analysis, Berlin, New York: Springer-Verlag, pp. 115–154, ISBN 978-3-540-13543-2, MR 0780040
  • Efremov, A. V. (1991), "Cell decompositions and the Novikov-Shubin invariants", Akademiya Nauk SSSR I Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk, 46 (3): 189–190, doi:10.1070/RM1991v046n03ABEH002800, ISSN 0042-1316, MR 1134099
  • Farber, Michael S. (1996), "Homological algebra of Novikov–Shubin invariants and Morse inequalities", Geometric and Functional Analysis, 6 (4): 628–665, CiteSeerX 10.1.1.252.2307, doi:10.1007/BF02247115, MR 1406667