横截面齐性叶状的次级特征类
几何拓扑
2015-05-22 v4 微分几何
摘要
设 G 为实秩为 1 的简单李群，S 为相应非紧型对称空间（H^n_R, H^n_C, H^n_H 或 H^2_O）的理想边界。我们证明了在固定流形上，其横截结构模型化为 G 在 S 上的作用的横截面齐性叶状，其次级特征类可能取值的有限性，除了 G=SO(n+1,1) 且 n 为偶数的情况。对于这个例外情况，我们构造了流形上打破有限性的叶状示例，并展示了一种较弱形式的有限性。这些是将 Brooks-Goldman 和 Heitsch 关于固定流形上横截面射影叶状的次级特征类有限性定理推广到其他横截结构的结果。我们还展示了计算某些叶状丛的 Godbillon-Vey 类的 Bott-Thurston-Heitsch 型公式，从而获得了双曲流形单位切球丛上横截面齐性叶状的刚性结果。
引用
@article{arxiv.1205.3375,
title = {Secondary characteristic classes of transversely homogeneous foliations},
author = {Jesús A. Álvarez López and Hiraku Nozawa},
journal= {arXiv preprint arXiv:1205.3375},
year = {2015}
}
备注
52 pages. Minor corrections in v2. Lemma 8.13 in v2 was wrong and erased in v3. Theorem 1.14 and Corollary 1.15-(ii) were accordingly corrected in v3. In v4, the constant r_G in Theorem 1.7 was corrected. The constant r_{F_4(-20)} is not included anymore, because it requires more detailed computation with special techniques on F_4. The formula (1.1) in Theorem 1.5 was corrected