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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.
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참고문헌 (33)
참고문헌 신청
A. Stipsicz / 2002 / Surface bundles with nonvanishing signature / Acta Math. Hungar 95 (4) : 299 ~ 307
B. Farb / 2012 / A primer on mapping class groups / Princeton University Press
B. Ozbagci / 2002 / Signatures of Lefschetz fibrations / Pacific J. Math 202 (1) : 99 ~ 118
B. Wajnryb / 1999 / An elementary approach to the mapping class group of a surface / Geom. Topol 3 : 405 ~ 466
C. T. C. Wall / 196
B. Farb / 2012 / A primer on mapping class groups / Princeton University Press
B. Ozbagci / 2002 / Signatures of Lefschetz fibrations / Pacific J. Math 202 (1) : 99 ~ 118
B. Wajnryb / 1999 / An elementary approach to the mapping class group of a surface / Geom. Topol 3 : 405 ~ 466
C. T. C. Wall / 196
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