Sections of surface bundles

Abstract

Let pW E !B be a bundle projection with base B and fibre F aspherical closed connected surfaces.We review what algebraic topology can tell us about such bundles and their total spaces and then consider criteria for p to have a section.In particular, we simplify the cohomological obstruction, and show that the transgression d 2 2;0 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.

Locations

• Geometry and topology monographs - View - PDF
• arXiv (Cornell University) - View - PDF
• DataCite API - View