2012/02/20 by Mario Listing, Listing, Mario · 1 citation
Mathematics · #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1202.4325
openalex publication_date 2012/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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^∞ --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.