2008/12/08 by Zadeh, Mostafa Esfahani
#19K56 #46L80 #53C21 #53C27 #58J22 #FOS: Mathematics #Geometric Topology (math.GT) #K-Theory and Homology (math.KT)
paper · doi:10.48550/arxiv.0812.1445
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 and J. Roe 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 the scalar curvature of g cannot be uniformly positive.