Real reflections, commutators, and cross-ratios in complex hyperbolic space

Julien Paupert; Pierre Will

doi:10.4171/GGD/398

Real reflections, commutators, and cross-ratios in complex hyperbolic space

Julien Paupert, Pierre Will

Mathematical and Statistical Sciences, School of (SoMSS)

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

13 Scopus citations

Abstract

We provide a concrete criterion to determine whether or not two given elements of PU.2; 1/ can bewritten as products of real reflections,with one reflection in common. As an application, we show that the Picardmodular groups PU(2, 1,O_d)with d = 1, 2, 3, 7, 11 are generated by real reflections up to index 1, 2, 4 or 8.

Original language	English (US)
Pages (from-to)	311-352
Number of pages	42
Journal	Groups, Geometry, and Dynamics
Volume	11
Issue number	1
DOIs	https://doi.org/10.4171/GGD/398
State	Published - 2017

Keywords

Complex hyperbolic geometry
Reflection groups

ASJC Scopus subject areas

Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.4171/GGD/398

Cite this

@article{e6b918a8b48a414b941f4dfa413e5318,

title = "Real reflections, commutators, and cross-ratios in complex hyperbolic space",

abstract = "We provide a concrete criterion to determine whether or not two given elements of PU.2; 1/ can bewritten as products of real reflections,with one reflection in common. As an application, we show that the Picardmodular groups PU(2, 1,Od)with d = 1, 2, 3, 7, 11 are generated by real reflections up to index 1, 2, 4 or 8.",

keywords = "Complex hyperbolic geometry, Reflection groups",

author = "Julien Paupert and Pierre Will",

note = "Publisher Copyright: {\textcopyright} European Mathematical Society.",

year = "2017",

doi = "10.4171/GGD/398",

language = "English (US)",

volume = "11",

pages = "311--352",

journal = "Groups, Geometry, and Dynamics",

issn = "1661-7207",

publisher = "European Mathematical Society Publishing House",

number = "1",

}

TY - JOUR

T1 - Real reflections, commutators, and cross-ratios in complex hyperbolic space

AU - Paupert, Julien

AU - Will, Pierre

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2017

Y1 - 2017

N2 - We provide a concrete criterion to determine whether or not two given elements of PU.2; 1/ can bewritten as products of real reflections,with one reflection in common. As an application, we show that the Picardmodular groups PU(2, 1,Od)with d = 1, 2, 3, 7, 11 are generated by real reflections up to index 1, 2, 4 or 8.

AB - We provide a concrete criterion to determine whether or not two given elements of PU.2; 1/ can bewritten as products of real reflections,with one reflection in common. As an application, we show that the Picardmodular groups PU(2, 1,Od)with d = 1, 2, 3, 7, 11 are generated by real reflections up to index 1, 2, 4 or 8.

KW - Complex hyperbolic geometry

KW - Reflection groups

UR - http://www.scopus.com/inward/record.url?scp=85019891694&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019891694&partnerID=8YFLogxK

U2 - 10.4171/GGD/398

DO - 10.4171/GGD/398

M3 - Article

AN - SCOPUS:85019891694

SN - 1661-7207

VL - 11

SP - 311

EP - 352

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

IS - 1

ER -

Real reflections, commutators, and cross-ratios in complex hyperbolic space

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this