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Signatures of surface bundles over surfaces Monden, Naoyuki
Description
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.
Item Metadata
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Signatures of surface bundles over surfaces
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-08-07T13:30
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Description |
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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Extent |
51 minutes
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Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Osaka Electro - Communication University
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Series | |
Date Available |
2018-02-03
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0363403
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International