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BIRS Workshop Lecture Videos

Signatures of surface bundles over surfaces Monden, Naoyuki


The Euler characteristic is multiplicative in fiber bundles. On the other hand, the signature is not. Atiyah and, independently, Kodaira showed it by giving surface bundles over surfaces with non-zero signatures. Since then, many examples with non-zero signatures have been constructed. The signature of a surface bundle over a surface has some restrictions, for examples, it is dividable by 4 and vanishes if the base genus is 0 or 1. Bryan and Donagi constructed examples over a genus-2 surface with non-zero signatures. The signatures and the genera of their examples are sporadic. In this talk, for any positive integer n, we give a surface bundle of fiber genus g over a surface of genus 2 with signature 4n and a section of self-intersection 0 if g is greater than or equal to 39n. Such example are constructed using mapping class group arguments.

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