Mark Walsh, National University of Ireland, Maynooth
Title: H-spaces, Loop spaces and k-Ricci Curvature
Abstract: In recent years, the problem of understanding the
topology of
spaces of Riemmanian Metrics on a smooth manifold M, which
satisfy
some particular curvature constraint, has attract considerable
attention.
We discuss some developments in this subject and show how
under
reasonable conditions, deeper algebraic structures such as
H-space and
loop space structure can be uncovered. In particular, we
discuss some
recent results concerning the space of positive k-Ricci
curvature metrics
on the sphere. These results are joint work with
David Wraith.