Valuations on manifolds and Rumin cohomology
- Bernig, Andreas Département de Mathématiques, Université de Fribourg, Switzerland
- Bröcker, Ludwig Mathematisches Institut, Universität Münster, Germany
-
2007
Published in:
- Journal of Differential Geometry. - 2007, vol. 75, no. 3, p. 433-457
English
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 Kaehler identities, the Rumin-de Rham complex and spectral geometry.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
-
- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
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- RERO DOC 8431
- DOI 10.4310/jdg/1175266280
- Persistent URL
- https://folia.unifr.ch/unifr/documents/300422
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