Bradley Burdick, University of California at Riverside

Title: The space of positive Ricci curvature metrics on spin manifolds.

Abstract: It is well known that the space of positive scalar
curvature metrics on a smooth manifold can have highly nontrivial
topology. The most basic feature of its topology is its connected
components. Using a variety of psc constructions, Carr was able to
construct a countable family of psc metrics on 4k-1 spheres that lie
in distinct path components. Using positive Ricci curvature surgery,
Wraith was able to construct a countable family of positive Ricci
curvature metrics that lie in the same path components as Carr's.
Using Gromov-Lawson's psc connected sum it is possible to construct a
countable family of psc metrics on any psc 4k-1 manifold, which for
spin manifolds will lie in distinct path components. In this talk we
will discuss how some of Perelman's ideas about positive Ricci
curvature connected combined with Wraith's work is able to construct a
countable family of positive Ricci curvature metrics on any 4k-1
manifold that admits a core metric, which for spin manifolds will lie
in distinct path components.