Small eigenvalues of the Conformal Laplacian

Details Small eigenvalues of the Conformal Laplacian Small eigenvalues of the Conformal Laplacian

2002-04-16

arxiv.org/abs/math/0204200v3

Geom. Funct. Anal. 13, 483-508 (2003)

Mathematics

Differential Geometry

Remark 3.3 added. To appear in "Geometric And Functional Analysis"

Scientific paper

10.1007/s00039-003-0419-6

We introduce a differential topological invariant for compact differentiable manifolds by counting the small eigenvalues of the Conformal Laplace operator. This invariant vanishes if and only if the manifold has a metric of positive scalar curvature. We show that the invariant does not increase under surgery of codimension at least three and we give lower and upper bounds in terms of the $\alpha$-genus.

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