Valuations on manifolds and rumin cohomology

Andreas Bernig D´epartement de Math´ematiques Ludwig Br¨ocker Fachbereich Mathematik und Informatik

Differential Geometry mathscidoc:1609.10012

Journal of Differential Geometry, 75, (3), 433-457, 2007
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 K¨ahler identities, the Rumin-de Rham complex and spectral geometry.
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@inproceedings{andreas2007valuations,
  title={VALUATIONS ON MANIFOLDS AND RUMIN COHOMOLOGY},
  author={Andreas Bernig, and Ludwig Br¨ocker},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160908194231122536669},
  booktitle={Journal of Differential Geometry},
  volume={75},
  number={3},
  pages={433-457},
  year={2007},
}
Andreas Bernig, and Ludwig Br¨ocker. VALUATIONS ON MANIFOLDS AND RUMIN COHOMOLOGY. 2007. Vol. 75. In Journal of Differential Geometry. pp.433-457. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160908194231122536669.
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