Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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SURFACE BUNDLES OVER SURFACES WITH A FIXED SIGNATURE

  • Lee, Ju A (Department of Mathematical Sciences Seoul National University)
  • Received : 2016.02.25
  • Published : 2017.03.01
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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

Acknowledgement

Supported by : National Research Foundation(NRF) of Korea

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