ID | 57752 |
FullText URL | |
Author |
Monden, Naoyuki
Department of Mathematics, Faculty of Science, Okayama University
Kaken ID
researchmap
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Abstract | The first aim of this paper is to give four types of examples of surface bundles over surfaces with non-zero signature. The first example is with base genus 2, a prescribed signature, a 0-section and the fiber genus greater than a certain number which depends on the signature. This provides a new upper bound on the minimal base genus for fixed signature and fiber genus. The second example gives a new asymptotic upper bound for this number in the case that fiber genus is odd. The third example has a small Euler characteristic. The last is a non-holomorphic example. The second aim is to improve upper bounds for stable commutator lengths of Dehn twists by giving factorizations of powers of Dehn twists as products of commutators. One of the factorizations is used to construct the second examples of surface bundles. As a corollary, we see that there is a gap between the stable commutator length of the Dehn twist along a non-separating curve in the mapping class group and that in the hyperelliptic mapping class group if the genus of the surface is greater than or equal to 8.
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Keywords | 57R22
57M07 (primary)
57R55
20F12
57N05 (secondary)
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Published Date | 2019-06-25
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Publication Title |
Journal of the London Mathematical Society. Second series
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Volume | volume100
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Issue | issue3
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Publisher | Wiley
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Start Page | 957
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End Page | 986
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ISSN | 0024-6107
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NCID | AA00701248
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Content Type |
Journal Article
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language |
English
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OAI-PMH Set |
岡山大学
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File Version | author
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DOI | |
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Related Url | isVersionOf https://doi.org/10.1112/jlms.12247
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