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The first Cohomology of Affine ℤ[supp] - actions on Tori and applications to rigidity.
- Source :
-
Bulletin of the Brazilian Mathematical Society . Jul2003, Vol. 34 Issue 2, p287-302. 16p. - Publication Year :
- 2003
-
Abstract
- Let φ a minimal affine Z[supp]-action on the torus T[supq], p ≥ 2 and q ≥ 1. The cohomology of φ (see definition below) depends on both the algebraic properties of the induced action on H[sup1](T[supq], Z) and the arithmetical properties of the translation cocycle. We give a Diophantine condition that characterizes those affine actions whose first cohomology group is finite dimensional. In this case it is necessarily isomorphic to R[supp]. Thus the R[supp]-action F[subφ] obtained by suspension of φ is parameter rigid, i.e., any other R[supp]-action with the same orbit foliation is smoothly conjugate to a reparametrization of F[subφ] by an automorphism of R[supp]. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16787544
- Volume :
- 34
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Brazilian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 11279954
- Full Text :
- https://doi.org/10.1007/s00574-003-0014-3