Surface bundles over surfaces with a fixed signature
Geometric Topology
2016-06-07 v2
Abstract
The signature of a surface bundle over a surface is known to be divisible by 4. It is also known that the signature vanishes if the fiber genus is less than or equal to 2 or the base genus is less than or equal to 1. In this article, we construct new smooth 4-manifolds with signature 4 which are surface bundles over surfaces with small fiber and base genera. From these we derive improved upper bounds for the minimal genus of surfaces representing the second homology classes of a mapping class group.
Cite
@article{arxiv.1511.06602,
title = {Surface bundles over surfaces with a fixed signature},
author = {Ju A Lee},
journal= {arXiv preprint arXiv:1511.06602},
year = {2016}
}
Comments
16 pages, 9 figures ; minor revisions in the proof of Prop 3.7, corrected some typos and citations