Construction of Acylindrical Hyperbolic 3-Manifolds with Quasifuchsian Boundary

Yongquan Zhang

doi:10.1080/10586458.2020.1718566

Construction of Acylindrical Hyperbolic 3-Manifolds with Quasifuchsian Boundary

Yongquan Zhang

Mathematical Science Institute

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We construct a one (real) dimensional deformation of an acylindrical hyperbolic 3-manifold, compute some associated arithmetic invariants and exhibit the skinning map along the deformation locus. The key idea is to construct a one-dimensional family of hyperbolic polyhedra; reflections in some of the faces of the polyhedra then generate a family of Kleinian groups.

Original language	English
Pages (from-to)	883-896
Number of pages	14
Journal	Experimental Mathematics
Volume	31
Issue number	3
DOIs	https://doi.org/10.1080/10586458.2020.1718566
State	Published - 2022

Keywords

Hyperbolic geometry
Hyperbolic polyhedron
Skinning map

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10.1080/10586458.2020.1718566

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title = "Construction of Acylindrical Hyperbolic 3-Manifolds with Quasifuchsian Boundary",

abstract = "We construct a one (real) dimensional deformation of an acylindrical hyperbolic 3-manifold, compute some associated arithmetic invariants and exhibit the skinning map along the deformation locus. The key idea is to construct a one-dimensional family of hyperbolic polyhedra; reflections in some of the faces of the polyhedra then generate a family of Kleinian groups.",

keywords = "Hyperbolic geometry, Hyperbolic polyhedron, Skinning map",

author = "Yongquan Zhang",

note = "Publisher Copyright: {\textcopyright} 2020 Taylor \& Francis Group, LLC.",

year = "2022",

doi = "10.1080/10586458.2020.1718566",

language = "English",

volume = "31",

pages = "883--896",

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T1 - Construction of Acylindrical Hyperbolic 3-Manifolds with Quasifuchsian Boundary

AU - Zhang, Yongquan

PY - 2022

Y1 - 2022

N2 - We construct a one (real) dimensional deformation of an acylindrical hyperbolic 3-manifold, compute some associated arithmetic invariants and exhibit the skinning map along the deformation locus. The key idea is to construct a one-dimensional family of hyperbolic polyhedra; reflections in some of the faces of the polyhedra then generate a family of Kleinian groups.

AB - We construct a one (real) dimensional deformation of an acylindrical hyperbolic 3-manifold, compute some associated arithmetic invariants and exhibit the skinning map along the deformation locus. The key idea is to construct a one-dimensional family of hyperbolic polyhedra; reflections in some of the faces of the polyhedra then generate a family of Kleinian groups.

KW - Hyperbolic geometry

KW - Hyperbolic polyhedron

KW - Skinning map

UR - https://www.scopus.com/pages/publications/85081227663

U2 - 10.1080/10586458.2020.1718566

DO - 10.1080/10586458.2020.1718566

M3 - Article

AN - SCOPUS:85081227663

SN - 1058-6458

VL - 31

SP - 883

EP - 896

JO - Experimental Mathematics

JF - Experimental Mathematics

IS - 3

ER -

Construction of Acylindrical Hyperbolic 3-Manifolds with Quasifuchsian Boundary

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