Let
be a bundle
projection with base
and fibre
aspherical closed connected surfaces. We review what algebraic topology can tell us
about such bundles and their total spaces and then consider criteria for
to have a
section. In particular, we simplify the cohomological obstruction, and show that the
transgression
in the homology LHS spectral sequence of a central extension is evaluation
of the extension class. We also give several examples of bundles without
sections.
