The moduli space of the modular group in complex hyperbolic geometry

被引：0

作者：

Elisha Falbel

John R. Parker

机构：

[1] Institut de Mathématiques,

[2] Université Pierre et Marie Curie,undefined

[3] 4,undefined

[4] place Jussieu,undefined

[5] F-75252 Paris,undefined

[6] France (e-mail: falbel@math.jussieu.fr),undefined

[7] Department of Mathematical Sciences,undefined

[8] University of Durham,undefined

[9] South Road,undefined

[10] Durham DH1 3LE,undefined

[11] England (e-mail: J.R.Parker@durham.ac.uk),undefined

来源：

Inventiones mathematicae | 2003年 / 152卷

关键词：

Modulus Space; Isometry Group; Modular Group; Fuchsian Group; Hyperbolic Geometry;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We construct the space of discrete, faithful, type-preserving representations of the modular group into the isometry group of complex hyperbolic 2-space up to conjugacy. This is the first Fuchsian group for which the entire complex hyperbolic deformation space has been constructed. We also show how the ℂ-spheres of Falbel-Zocca are related to the ℝ-spheres (hybrid spheres) of Schwartz.

引用

页码：57 / 88

页数：31

共 50 条

[21] GEOMETRY OF THE SUPERCONFORMAL MODULI SPACE
BARANOV, MA
FROLOV, IV
SHVARTS, AS
THEORETICAL AND MATHEMATICAL PHYSICS, 1989, 79 (02) : 509 - 517
[22] The moduli space of hyperbolic cone structures
Zhou, Q
JOURNAL OF DIFFERENTIAL GEOMETRY, 1999, 51 (03) : 517 - 550
[23] ON THE MODULI SPACE OF THE T(6)/Z(3) ORBIFOLD AND ITS MODULAR GROUP
FERRARA, S
FRE, P
SORIANI, P
CLASSICAL AND QUANTUM GRAVITY, 1992, 9 (07) : 1649 - 1661
[24] THE MODULI SPACE OF POINTS IN THE BOUNDARY OF QUATERNIONIC HYPERBOLIC SPACE
Gou, Gaoshun
Jiang, Yueping
OSAKA JOURNAL OF MATHEMATICS, 2020, 57 (04) : 827 - 846
[25] MODULAR INVARIANCE AND COMPACTIFICATION OF THE MODULI SPACE
GOMEZ, C
PHYSICS LETTERS B, 1986, 175 (01) : 32 - 36
[26] Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group
Oh, YG
DUKE MATHEMATICAL JOURNAL, 2005, 130 (02) : 199 - 295
[27] Hyperbolic geometry and moduli of real curves of genus three
Gert Heckman
Sander Rieken
Mathematische Annalen, 2018, 370 : 1321 - 1360
[28] Hyperbolic geometry and moduli of real curves of genus three
Heckman, Gert
Rieken, Sander
MATHEMATISCHE ANNALEN, 2018, 370 (3-4) : 1321 - 1360
[29] Moduli space of extrinsic circular trajectories on real hypersurfaces of type (A2) in a complex hyperbolic space
Aoki, Yusei
Adachi, Toshiaki
NOTE DI MATEMATICA, 2022, 42 (01): : 77 - 94
[30] Horospherical geometry in the hyperbolic space
Izumiya, Shyuichi
NONCOMMUTATIVITY AND SINGULARITIES: PROCEEDINGS OF FRENCH-JAPANESE SYMPOSIA HELD AT IHES IN 2006, 2009, 55 : 31 - 49

← 1 2 3 4 5 →