Novikov–Shubin invariant

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

Notes

References

• Cheeger, Jeff; Gromov, Mikhael (1985), "On the characteristic numbers of complete manifolds of bounded curvature and finite volume", in Chavel, Isaac; Farkas, Hershel M., Differential geometry and complex analysis, Berlin, New York: Springer-Verlag, pp. 115–154, ISBN 978-3-540-13543-2, MR 780040 

• 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, ISSN 0042-1316, MR 1134099, doi:10.1070/RM1991v046n03ABEH002800 

• Gromov, Mikhail; Shubin, M. A. (1991), "von Neumann spectra near zero", Geometric and Functional Analysis, 1 (4): 375–404, ISSN 1016-443X, MR 1132295, doi:10.1007/BF01895640 

• Lück, Wolfgang (2002). L²-invariants: theory and applications to geometry and K-theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]. 44. Berlin: Springer-Verlag. ISBN 3-540-43566-2. 

• Novikov, S. P.; Shubin, M. A. (1986), "Morse inequalities and von Neumann II₁-factors", Doklady Akademii Nauk SSSR, 289 (2): 289–292, ISSN 0002-3264, MR 856461