In
mathematics, a Novikov–Shubin invariant, introduced by , is an invariant of a compact
Riemannian manifold related to the
spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
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 topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from grc, ὁμός "same, similar" and "place") if one can be "continuously deformed" into the other, such a defor ...
. In particular, it does not depend on the chosen Riemannian metric on the manifold.
Notes
References
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Differential geometry
Algebraic topology
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