Volume 19 (2015)

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ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Sections of surface bundles

Jonathan A Hillman

Geometry & Topology Monographs 19 (2015) 1–19

arXiv: 1309.3803

Abstract

Let p: 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 d2,02 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.

Keywords
factor set, extension, lantern relation, section, surface bundle, transgression
Mathematical Subject Classification 2010
Primary: 20K35
Secondary: 55R10, 57N13
References
Publication
Received: 13 November 2014
Accepted: 15 November 2014
Published: 29 December 2015
Authors
Jonathan A Hillman
School of Mathematics and Statistics
University of Sydney
Sydney, NSW 2006
Australia