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http://dx.doi.org/10.4134/JKMS.j160126

SURFACE BUNDLES OVER SURFACES WITH A FIXED SIGNATURE  

Lee, Ju A (Department of Mathematical Sciences Seoul National University)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.2, 2017 , pp. 545-561 More about this Journal
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 ${\leq}2$ or the base genus ${\leq}1$. 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.
Keywords
surface bundle; mapping class group; signature; Lefschetz fibration;
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