Journal of Noncommutative Geometry

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Volume 4, Issue 3, 2010, pp. 459–473
DOI: 10.4171/JNCG/63

Published online: 2010-07-26

Index theory and partitioning by enlargeable hypersurfaces

Mostafa Esfahani Zadeh[1]

(1) University of Göttingen, Germany

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.

Keywords: Higher index theory, enlargeablity, Dirac operators

Zadeh Mostafa Esfahani: Index theory and partitioning by enlargeable hypersurfaces. J. Noncommut. Geom. 4 (2010), 459-473. doi: 10.4171/JNCG/63