Journal article

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
Persistent URL
https://folia.unifr.ch/unifr/documents/300422
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