Signatures of foliated surface bundles and the symplectomorphism groups of surfaces
Signatures of foliated surface bundles and the symplectomorphism groups of surfaces
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DOI：
10.1016/j.top.2004.05.002
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发表时间：
2003-05
期刊：
影响因子：
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通讯作者：
D. Kotschick;S. Morita
中科院分区：
文献类型：
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作者：
D. Kotschick;S. Morita
对于亏格g ∈ 3的任意闭定向曲面，证明了在全空间的特征标不为零的曲面上存在叶状的定向丛。我们可以安排水平叶理的全完整性在纤维上保持一个规定的辛形式ω。我们将横辛形式表示的上同调类与交叉同态Flux：Symp g→H1（g; R）联系起来，交叉同态Flux：Symp g → H1（g; R）是Flux同态Flux：Symp g→H1（g; R）从单位分量Symp g到关于辛形式ω的Symp g的辛同态的整个群Symp g的扩展。
For any closed oriented surface Σgof genus g⩾3, we prove the existence of foliatedΣg-bundles over surfaces such that the signatures of the total spaces are non-zero. We can arrange that the total holonomy of the horizontal foliations preserve a prescribed symplectic form ω on the fiber. We relate the cohomology class represented by the transverse symplectic form to a crossed homomorphism Flux : Symp Σg→H1(Σg; R ) which is an extension of the flux homomorphism Flux : Symp0Σg→H1(Σg; R ) from the identity component Symp0Σgto the whole group Symp Σgof symplectomorphisms of Σgwith respect to the symplectic form ω.