Small eigenvalues of the Conformal Laplacian

Christian Baer, Mattias Dahl

Published 2002-04-16, updated 2002-12-03Version 3

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.