Title:
Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
Abstract: I will discuss joint work with C. Li and
Y. Liokumovich in which we classify (up to homotopy) 4 dimensional
compact manifolds with π2 = 0 that admit Riemannian metrics of
positive scalar curvature. Namely, after passing to a finite cover,
such a manifold is homotopy equivalent to S4 or a connect sum of S3
x S1's. (The analogous statement holds for 5-dimensional manifolds
with π2 =π3 =0).