Alladi Ramakrishnan Hall

Geometry of Metric Bundles

Pranab Sardar

UC Davis

Metric bundles are a coarse-geometric generalization of the
notion of fiber
bundles in topology where fibers are quasi-isometric geodesic metric
spaces; as for
local triviality, uniformly close fibers are uniformly quasi-isometric.
We prove the existence of quasi-isometric sections when the fibers are
'non-elementary'
hyperbolic metric spaces. Then we prove a combination theorem for metric
bundles that
gives sufficient conditions for a metric bundle with hyperbolic fibers and
base to be hyper
-bolic. Time permitting, we shall see some applications of this theorem
too.