Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 58 min ago
Peer-reviewedCC BYGeometry & Topology

Gromov–Thurston manifolds and anti-de Sitter geometry

  • Daniel Monclair1,2
  • Jean‐Marc Schlenker3,4
  • Nicolas Tholozan5,6,7,8
8 affiliations
  1. 1Université Paris-Saclay, Laboratoire de Mathématiques d’Orsay, Orsay, France
  2. 2LMO - Laboratoire de Mathématiques d'Orsay (Bâtiment 307, 91405, Orsay cedex - France)
  3. 3University of Luxembourg, FTSM, Department of Mathematics, Esch-sur-Alzette, Luxembourg
  4. 4uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg (Université du Luxembourg [Siège] – 2, place de l’Université – L-4365 Esch-sur-Alzette – Luxembourg - Luxembourg)
  5. 5CNRS, École Normale Supérieure, PSL, Paris, France
  6. 6Algèbre et Géométrie (DMA) (45 rue d'Ulm 75005 Paris - France)
  7. 7CNRS - Centre National de la Recherche Scientifique (France)
  8. 8ENS-PSL - École normale supérieure - Paris (45, Rue d'Ulm - 75230 Paris cedex 05 - France)
Open at sourcePDFDOICite

Abstract

We consider hyperbolic and anti-de Sitter (AdS) structures on M .0;1/, where M is a d -dimensional Gromov-Thurston manifold.If M has cone angles greater than 2 , we show that there exists a "quasifuchsian" (globally hyperbolic maximal) AdS manifold such that the future boundary of the convex core is isometric to M .When M has cone angles less than 2 , there exists a hyperbolic end with boundary a concave pleated surface isometric to M.Moreover, in both cases, if M is a Gromov-Thurston manifold with 2k pieces (as defined below), the moduli space of quasifuchsian AdS structures (resp.hyperbolic ends) satisfying this condition contains a submanifold of dimension 2k 3.When d D 3, the moduli space of quasifuchsian AdS (resp.hyperbolic) manifolds diffeomorphic to M .0;1/ contains a submanifold of dimension 2k 2, and extends up to a "Fuchsian" manifold; that is, an AdS (resp.hyperbolic) warped product of a closed hyperbolic manifold by R.We then use this construction of quasifuchsian AdS manifolds to obtain new compact quotients of O.2d; 2/=U.d;1/.The construction uses an explicit correspondence between quasifuchsian .2dC1/dimensionalAdS manifolds and compact quotients of O.2d; 2/=U.d;1/, which we interpret as the space of timelike geodesic Killing fields of AdS 2d C1 .

Related

  1. Thurston's sphere packing on 3-dimensional manifolds, II
    Xiaokai He, Xu Xu, Chao Zheng
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  2. Cannon-Thurston Maps, Harmonic Maps, and Minimal Surfaces in Fibered Hyperbolic 3-Manifolds
    Alberto Verjovsky
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  3. Gromov-Hausdorff instability of the positive mass theorem for Kähler manifolds
    Romy Marie Merkel
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  4. Gromov-Hausdorff Stability and Rigidity of manifolds via Heisenberg-Pauli-Weyl Uncertainty Principle
    Mousomi Bhakta, Debdip Ganguly, Debabrata Karmakar
    arXivPreprintCC BY-NC-SA 4.0Full textAnalysis & PDEsGeometry & topologyarXiv
  5. On (2,1)-dimensional anti-de Sitter spacetimes with convex boundary
    Roman Prosanov, Jean-Marc Schlenker, Graham Andrew Smith
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@article{monclair2026gromovthurston,
  title = {{Gromov–Thurston manifolds and anti-de Sitter geometry}},
  author = {Daniel Monclair and Jean‐Marc Schlenker and Nicolas Tholozan},
  journal = {Geometry \& Topology},
  year = {2026},
  month = jul,
  doi = {10.2140/gt.2026.30.2097},
  url = {https://doi.org/10.2140/gt.2026.30.2097},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Gromov–Thurston manifolds and anti-de Sitter geometry
AU  - Daniel Monclair
AU  - Jean‐Marc Schlenker
AU  - Nicolas Tholozan
PY  - 2026
DA  - 2026/07/31
JO  - Geometry & Topology
DO  - 10.2140/gt.2026.30.2097
UR  - https://doi.org/10.2140/gt.2026.30.2097
AB  - We consider hyperbolic and anti-de Sitter (AdS) structures on M .0;1/, where M is a d -dimensional Gromov-Thurston manifold.If M has cone angles greater than 2 , we show that there exists a "quasifuchsian" (globally hyperbolic maximal) AdS manifold such that the future boundary of the convex core is isometric to M .When M has cone angles less than 2 , there exists a hyperbolic end with boundary a concave pleated surface isometric to M.Moreover, in both cases, if M is a Gromov-Thurston manifold with 2k pieces (as defined below), the moduli space of quasifuchsian AdS structures (resp.hyperbolic ends) satisfying this condition contains a submanifold of dimension 2k 3.When d D 3, the moduli space of quasifuchsian AdS (resp.hyperbolic) manifolds diffeomorphic to M .0;1/ contains a submanifold of dimension 2k 2, and extends up to a "Fuchsian" manifold; that is, an AdS (resp.hyperbolic) warped product of a closed hyperbolic manifold by R.We then use this construction of quasifuchsian AdS manifolds to obtain new compact quotients of O.2d; 2/=U.d;1/.The construction uses an explicit correspondence between quasifuchsian .2dC1/dimensionalAdS manifolds and compact quotients of O.2d; 2/=U.d;1/, which we interpret as the space of timelike geodesic Killing fields of AdS 2d C1 .
SN  - 1364-0380
SN  - 1465-3060
ER  -