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SURFACE BUNDLES OVER SURFACES WITH A FIXED SIGNATURE

이주아
대한수학회 (The Korean Mathematical Society)|2017.03|대한수학회지 (Journal of the KMS)|제54권 제2호|pp. 545-561

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참고문헌

키워드

signaturemapping class groupLefschetz fibrationsurface bundle
주제분류수학

초록

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.

Abstract

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.

참고문헌 (33)

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