A K-theoretic codimension 2 obstruction to positive scalar curvature

10 November 2008
Thomas Schick
Let M be a closed spin manifold. Gromov and Lawson have shown that the presence of certain "enlargeable" submanifolds of codimension 2 is an obstruction to the existence of a Riemannian metric with positive scalar curvature on M. In joint work with Hanke, we refine the geoemtric condition of "enlargeability": it suffices that a K-theoretic index obstruction of the submanifold doesn't vanish. A "folk conjecture" asserts that all index type obstructions to positive scalar curvature should be read off from the corresponding index for the ambient manifold M (this this is equivalent to a small part of the strong Novikov conjecture). We address this question for the obstruction above and discuss partial results.
  • Geometry and Analysis Seminar