Colloquium abstracts

F.T. Farrell
Binghamton University, USA
May 7, 2012

Bundles with negatively curved fibers:  This talk is a report on joint work with Pedro Ontaneda. Let $M$ be a closed smooth manifold which can support a Riemannian metric with sectional curvatures all negative: e.g. a hyperbolic metric. We are interested in smooth $M$-bundles $p:E \to B$ whose abstract fiber is $M$; but all of whose specific fibers $p^{-1}(x)$, $x$ in $B$, are equipped with negatively curved Riemannian metrics $b_x$, which vary continuously with $x$. This is called a bundle with negatively curved fibers. We analyze the forget extra structure map from bundles with negatively curved fibers $M$ to smooth $M$-bundles.