# Index theory and partitioning by enlargeable hypersurfaces

### Mostafa Esfahani Zadeh

University of Göttingen, Germany

## Abstract

In this paper we state and prove a higher index theorem for an odd-dimensional connected spin Riemannian manifold (M,g) which is partitioned by an oriented closed hypersurface N. This index theorem generalizes a theorem due to N. Higson in the context of Hilbert modules. Then we apply this theorem to prove that if N is area-enlargeable and if there is a smooth map from M into N such that its restriction to N has non-zero degree, then the scalar curvature of g cannot be uniformly positive.

## Cite this article

Mostafa Esfahani Zadeh, Index theory and partitioning by enlargeable hypersurfaces. J. Noncommut. Geom. 4 (2010), no. 3, pp. 459–473

DOI 10.4171/JNCG/63