Local rigidity of restrictions of Weyl chamber flows

Damjanović, Danijela; Katok, Anatole

doi:10.1016/j.crma.2007.03.009

Cited by 9 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the last two decades, it has been found that there exist locally rigid actions of higher dimensional Lie groups, and the rigidity theory of locally free actions have been rapidly developed. The reader can find examples of locally rigid or parameter rigid actions in many papers [5,9,10,11,12,49,51,18,24,32,33,36,41,42,52,53], some of which we will discuss in this article.…”

Section: Introductionmentioning

confidence: 99%

Deformation of locally free actions and the leafwise cohomology

Asaoka¹

2010

Preprint

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 99%

Deformation of locally free actions and the leafwise cohomology

Asaoka¹

2010

Preprint

View full text Add to dashboard Cite

“…In ergodic theoretic applications p(Γ\G) controls the precise mixing rate of the action of noncompact subgroups of G on Γ\G [36,19,42]. In questions of local rigidity of related actions the spectral gap controls the "small divisors" in the linearized co-cycle equations [12] and it plays an important role in the study of the cohomology of Γ [3,4]. The congruence case is defined as follows.…”

Section: Introductionmentioning

confidence: 99%

Strong Spectral Gaps for Compact Quotients of Products of $\PSL(2,\bbR)$

Kelmer,

Sarnak

2008

Preprint

View full text Add to dashboard Cite

The existence of a strong spectral gap for quotients Γ\G of noncompact connected semisimple Lie groups is crucial in many applications. For congruence lattices there are uniform and very good bounds for the spectral gap coming from the known bounds towards the Ramanujan-Selberg Conjectures. If G has no compact factors then for general lattices a strong spectral gap can still be established, however, there is no uniformity and no effective bounds are known. This note is concerned with the strong spectral gap for an irreducible co-compact lattice Γ in G = PSL(2, R) d for d ≥ 2 which is the simplest and most basic case where the congruence subgroup property is not known. The method used here gives effective bounds for the spectral gap in this setting.

show abstract

“…In ergodic-theoretic applications p( \G) controls the precise mixing rate of the action of noncompact subgroups of G on \G [36,19,42]. In questions of local rigidity of related actions the spectral gap controls the "small divisors" in the linearized cocycle equations [12] and it plays an important role in the study of the cohomology of [3,4].…”

Section: Introductionmentioning

confidence: 99%

Strong spectral gaps for compact quotients of products of PSL(2,ℝ)

Kelmer

Sarnak²

2009

J. Eur. Math. Soc.

View full text Add to dashboard Cite

Abstract. The existence of a strong spectral gap for quotients \G of noncompact connected semisimple Lie groups is crucial in many applications. For congruence lattices there are uniform and very good bounds for the spectral gap coming from the known bounds towards the RamanujanSelberg conjectures. If G has no compact factors then for general lattices a spectral gap can still be established, but there is no uniformity and no effective bounds are known. This note is concerned with the spectral gap for an irreducible co-compact lattice in G = PSL(2, R) d for d ≥ 2, which is the simplest and most basic case where the congruence subgroup property is not known. The method used here gives effective bounds for the spectral gap in this setting.

show abstract

Local rigidity of restrictions of Weyl chamber flows

Cited by 9 publications

References 9 publications

Deformation of locally free actions and the leafwise cohomology

Deformation of locally free actions and the leafwise cohomology

Strong Spectral Gaps for Compact Quotients of Products of $\PSL(2,\bbR)$

Strong spectral gaps for compact quotients of products of PSL(2,ℝ)

Contact Info

Product

Resources

About