Valuations on manifolds and Rumin cohomology
Valuations on manifolds and Rumin cohomology
复制标题
流形和 Rumin 上同调的评估
DOI：
10.4310/jdg/1175266280
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发表时间：
2007
影响因子：
2.5
通讯作者：
L. Bröcker
中科院分区：
文献类型：
--
作者：
A. Bernig;L. Bröcker
通过与共球丛的Rumin-de Rham复形建立联系，研究了流形上的光滑赋值。微分形式上的几种运算导出了光滑赋值上的运算：签名算子、Rumin-Laplace算子、Euler-Verdier对合和导子算子。作为应用，将有限维欧氏空间上偶平移不变赋值的Alesker硬Lefschetz定理推广到所有平移不变赋值。证明使用Kähler恒等式，Rumin-de Rham复形和谱几何。
Smooth valuations on manifolds are studied by establishing a link with the Rumin-de Rham complex of the co-sphere bundle. Several operations on differential forms induce operations on smooth valuations: signature operator, Rumin-Laplace operator, Euler-Verdier involution and derivation operator. As an application, Alesker’s Hard Lefschetz Theorem for even translation invariant valuations on a finite-dimensional Euclidean space is generalized to all translation invariant valuations. The proof uses Kähler identities, the Rumin-de Rham complex and spectral geometry.