Open Access
March 2007 Valuations on manifolds and Rumin cohomology
A. Bernig, L. Bröcker
J. Differential Geom. 75(3): 433-457 (March 2007). DOI: 10.4310/jdg/1175266280


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.


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A. Bernig. L. Bröcker. "Valuations on manifolds and Rumin cohomology." J. Differential Geom. 75 (3) 433 - 457, March 2007.


Published: March 2007
First available in Project Euclid: 30 March 2007

zbMATH: 1117.58005
MathSciNet: MR2301452
Digital Object Identifier: 10.4310/jdg/1175266280

Rights: Copyright © 2007 Lehigh University

Vol.75 • No. 3 • March 2007
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