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A TOPOLOGICAL CRITERION FOR THE EXISTENCE OF HALF-BOUND STATES

Published online by Cambridge University Press:  24 March 2003

GILLES CARRON
GILLES CARRON
Affiliation:
Département de Mathématiques, UMR 6629, Université de Nantes, 2 rue de la Houssinière, F-44322 Nantes Cedex 03, [email protected]
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Abstract

The following theorem is proved: if $(M^{4n+1},g)$ is a complete Riemannian manifold and $\Sigma\subset M$ is an oriented hypersurface partitioning $M$ and with non-zero signature, then the spectrum of the Hodge–deRham Laplacian is $[0,\infty[$ . This result is obtained by a new Callias-type index. This new formula links half-bound harmonic forms (that is, nearly $L^2$ but not in $L^2$ ) with the signature of $\Sigma$ .

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 3 , June 2002 , pp. 757 - 768
Copyright
The London Mathematical Society, 2002

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