Geodesic
Vanishing of cohomology and parameter rigidity of actions of solvable Lie groups
Maruhashi, Hirokazu1
1 Max Planck Institute for Mathematics, Vivatsgasse 7, D-53111 Bonn, Germany
Geometry & topology, Tome 21 (2017) no. 1, pp. 157-191.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We give a sufficient condition for parameter rigidity of actions of solvable Lie groups, by vanishing of (uncountably many) first cohomologies of the orbit foliations. In some cases, we can prove that vanishing of finitely many cohomologies is sufficient. For this purpose we use a rigidity property of quasiisometry.

As an application we prove some actions of 2-step solvable Lie groups on mapping tori are parameter rigid. Special cases of these actions are considered in a paper of Matsumoto and Mitsumatsu.

We also remark on the relation between transitive locally free actions of solvable Lie groups and lattices in solvable Lie groups, and apply results in rigidity theory of lattices in solvable Lie groups to construct transitive locally free actions with some properties.

DOI : 10.2140/gt.2017.21.157
Classification : 37A20, 37C15, 37C85
Keywords: parameter rigidity, solvable Lie groups, leafwise cohomology, quasiisometry

Maruhashi, Hirokazu 1

1 Max Planck Institute for Mathematics, Vivatsgasse 7, D-53111 Bonn, Germany 
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Maruhashi, Hirokazu. Vanishing of cohomology and parameter rigidity of actions of solvable Lie groups. Geometry & topology, Tome 21 (2017) no. 1, pp. 157-191. doi : 10.2140/gt.2017.21.157. http://geodesic.mathdoc.fr/articles/10.2140/gt.2017.21.157/

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