#### 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.

Done