start-ver=1.4
cd-journal=joma
no-vol=100
cd-vols=
no-issue=3
article-no=
start-page=957
end-page=986
dt-received=
dt-revised=
dt-accepted=
dt-pub-year=2019
dt-pub=20190625
dt-online=
en-article=
kn-article=
en-subject=
kn-subject=
en-title=
kn-title=Signatures of surface bundles and scl of a Dehn twist
en-subtitle=
kn-subtitle=
en-abstract=
kn-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.
en-copyright=
kn-copyright=

en-aut-name=MondenNaoyuki
en-aut-sei=Monden
en-aut-mei=Naoyuki
kn-aut-name=
kn-aut-sei=
kn-aut-mei=
aut-affil-num=1
ORCID=

affil-num=1
en-affil=Department of Mathematics, Faculty of Science, Okayama University
kn-affil=
en-keyword=57R22
kn-keyword=57R22
en-keyword=57M07 (primary)
kn-keyword=57M07 (primary)
en-keyword=57R55
kn-keyword=57R55
en-keyword=20F12
kn-keyword=20F12
en-keyword=57N05 (secondary)
kn-keyword=57N05 (secondary)
END