Scalar curvature and vector bundles

Abstract

In the first part we use Gromov's K--area to define the K--area homology which stabilizes into singular homology on the category of pairs of compact smooth manifolds. The second part treats the questions of certain curvature gaps. For instance, the $L^{\infty }$--curvature gap of complex vector bundles on a compact manifold is positive if and only if the K--area homology coincides with the reduced singular homology in all even degrees. In the third part we give some upper bounds of the scalar curvature on compact manifolds. In particular, we generalize results by Llarull and Goette, Semmelmann.

arXiv admin note: substantial text overlap with arXiv:1007.3166

References in corpus (8)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Einstein manifolds with nonnegative isotropic curvature are locally symmetric
• Enlargeability and index theory: Infinite covers
• Large and small group homology
• Scalar Curvature on Compact Symmetric Spaces
• Scalar Curvature Estimates by Parallel Alternating Torsion
• Infinite connected sums, K-area and positive scalar curvature

Cited by in corpus (2)

• A modified Yamabe invariant and a Hopf conjecture
• Relative K-area homology and applications