The pressure metric on the Margulis multiverse

Ghosh, Sourav

doi:10.1007/s10711-017-0260-y

Cited by 7 publications

(13 citation statements)

References 51 publications

(129 reference statements)

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“…In this article we define affine crossratios for any four mutually transverse affine null planes in R 2n−1 and in Propositions 2.3.2 and 2.3.1 we show how they are intimately related with Margulis invariants. Similar results in the case of dimension three were found by Charette-Drumm in [CD04] and by Ghosh in [Gho17b]. Moreover, in Proposition 2.4.2, we also provide nice algebraic expressions for the linear counterparts, in SO 0 (n, n), of these affine crossratios.…”

Section: Introductionsupporting

confidence: 84%

“…We have also proved in Proposition 2.3.5 similar results regarding Margulis invariants. These expressions in the case of dimension three was already known by works of Charette-Drumm [CD04] and Ghosh [Gho17b].…”

Section: Introductionmentioning

confidence: 71%

“…Moreover, it follows from our construction that this collection of norms satisfy all the first three conditions listed above. More details about properties of these kind of constructions can be found in [HPS06] and [Shu87] (see also [Gho17b,Gho17a] and [BCLS15]).…”

Section: Avatars Of Margulis Invariantsmentioning

confidence: 99%

“…Further dynamical properties of these representations were proved by Bridgeman-Canary-Labourie-Sambarino in [BCLS15]. Moreover, the notion of an affine Anosov representation was introduced recently in the works of Ghosh [Gho17b,Gho17a] and , to define appropriate notions of Anosov representations into affine groups of the form SO 0 (n − 1, n) ⋉ R 2n−1 .…”

Section: Introductionmentioning

confidence: 99%

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Avatars of Margulis invariants and proper actions

Ghosh¹

2018

Preprint

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In this article, we interpret affine Anosov representations of any word hyperbolic group in SO0(n − 1, n) ⋉ R 2n−1 as infinitesimal versions of representations of word hyperbolic groups in SO0(n, n) which are both Anosov in SO0(n, n) with respect to the stabilizer of an oriented (n−1)-dimensional isotropic plane and Anosov in SL(2n, R) with respect to the stabilizer of an oriented n-dimensional plane. Moreover, we show that representations of word hyperbolic groups in SO0(n, n) which are Anosov in SO0(n, n) with respect to the stabilizer of an oriented (n − 1)dimensional isotropic plane, are Anosov in SL(2n, R) with respect to the stabilizer of an oriented n-dimensional plane if and only if its action on SO0(n, n)/SO0(n − 1, n) is proper. In the process, we also provide various different interpretations of the Margulis invariant.

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Section: Introductionsupporting

confidence: 84%

Section: Introductionmentioning

confidence: 71%

Section: Avatars Of Margulis Invariantsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Avatars of Margulis invariants and proper actions

Ghosh¹

2018

Preprint

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“…Ghosh [32] used work of Goldman, Labourie and Margulis [34,35] to interpret holonomy maps of Margulis space times (without cusps) as "Anosov representations" into the (non-semisimple) Lie group Aff(R 3 ) of affine automorphisms of R 3 . Ghosh [33] was then able to adapt the techniques of [17] to produce a pressure form on the analytic manifold M of (conjugacy classes of) holonomy maps of Margulis space times of fixed rank (with no cusps). This pressure form is an analytic Riemannian metric on the slice M k of M consisting of holonomy maps with entropy k (see Ghosh [33, Thm.…”

Section: Generalizations and Consequencesmentioning

confidence: 99%

An introduction to pressure metrics for higher Teichmüller spaces

Bridgeman

Canary

Sambarino

2017

Ergod. Th. Dynam. Sys.

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We discuss how one uses the thermodynamic formalism to produce metrics on higher Teichmüller spaces. Our higher Teichmüller spaces will be spaces of Anosov representations of a word-hyperbolic group into a semi-simple Lie group. We begin by discussing our construction in the classical setting of the Teichmüller space of a closed orientable surface of genus at least 2, then we explain the construction for Hitchin components and finally we treat the general case. This paper surveys results of Bridgeman, Canary, Labourie and Sambarino, The pressure metric for Anosov representations, and discusses questions and open problems which arise.

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Margulis multiverse: Infinitesimal rigidity, pressure form and convexity

Ghosh

2023

Trans. Amer. Math. Soc.

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In this article we construct the pressure forms on the moduli spaces of higher dimensional Margulis spacetimes without cusps and study their properties. We show that the Margulis spacetimes are infinitesimally determined by their marked Margulis invariant spectra. We use this fact to show that the restrictions of the pressure form give Riemannian metrics on the constant entropy sections of the quotient moduli space. We also show that constant entropy sections of the moduli space with fixed linear parts bound convex domains.

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The pressure metric on the Margulis multiverse

Abstract: This paper defines the pressure metric on the Moduli space of Margulis spacetimes without cusps and shows that it is positive definite on the constant entropy sections. It also demonstrates an identity regarding the variation of the cross-ratios.Date: September 12, 2018.

Cited by 7 publications

References 51 publications

Avatars of Margulis invariants and proper actions

Avatars of Margulis invariants and proper actions

An introduction to pressure metrics for higher Teichmüller spaces

Margulis multiverse: Infinitesimal rigidity, pressure form and convexity

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