Finanzierung: Deutsche Forschungsgemeinschaft (DFG)
Laufzeit: 2 Jahre (2005-2007)
Zusammenfassung: This succeeds our project with the same title
during the first phase of the Schwerpunktprogramm.
We shall investigate the question which oriented closed smooth manifolds
M admit metrics of positive scalar curvature. If M is
spin, we continue our work on establishing relations between
the enlargeability obstruction
against positive scalar curvature due to Gromov and Lawson and
the universal index obstruction with values in the K-theory
of the maximal C*-algebra of the fundamental group of M
due to Rosenberg. Furthermore, we
study the Rosenberg index for 3-dimensional manifolds that
contain essential circles. Another direction of research
is an investigation on relations of the positive scalar
curvature question with the coarse type of the underlying manifold.