Semialgebraic description of Teichmüller space

Yohei Komori

doi:10.2977/prims/1195145147

Semialgebraic description of Teichmüller space

Yohei Komori^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

We give a concrete semialgebraic description of Teichmüller space T_g of the closed surface group Γ_g of genus g(≥2). Our result implies that for any SL₂(R)-representation of Γ_g, we can determine whether this representation is discrete and faithful or not by using 4g-6 explicit trace inequalities. We also show the connectivity and contractibility of T_g from the point of view of SL₂(R)-representations of Γ_g. Previously, these properties of T_g had been proved by using hyperbolic geometry and quasi-conformal deformations of Fuchsian groups. Our method is simple and only uses topological properties of the space of SL₂(R)-representations of Γ_g.

Original language	English
Pages (from-to)	527-571
Number of pages	45
Journal	Publications of the Research Institute for Mathematical Sciences
Volume	33
Issue number	4
DOIs	https://doi.org/10.2977/prims/1195145147
Publication status	Published - 1997 Dec
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.2977/prims/1195145147

Cite this

@article{fc8acb0e113344caa5188bd5c447b419,

title = "Semialgebraic description of Teichm{\"u}ller space",

abstract = "We give a concrete semialgebraic description of Teichm{\"u}ller space Tg of the closed surface group Γg of genus g(≥2). Our result implies that for any SL2(R)-representation of Γg, we can determine whether this representation is discrete and faithful or not by using 4g-6 explicit trace inequalities. We also show the connectivity and contractibility of Tg from the point of view of SL2(R)-representations of Γg. Previously, these properties of Tg had been proved by using hyperbolic geometry and quasi-conformal deformations of Fuchsian groups. Our method is simple and only uses topological properties of the space of SL2(R)-representations of Γg.",

author = "Yohei Komori",

year = "1997",

month = dec,

doi = "10.2977/prims/1195145147",

language = "English",

volume = "33",

pages = "527--571",

journal = "Publications of the Research Institute for Mathematical Sciences",

issn = "0034-5318",

publisher = "European Mathematical Society Publishing House",

number = "4",

}

TY - JOUR

T1 - Semialgebraic description of Teichmüller space

AU - Komori, Yohei

PY - 1997/12

Y1 - 1997/12

N2 - We give a concrete semialgebraic description of Teichmüller space Tg of the closed surface group Γg of genus g(≥2). Our result implies that for any SL2(R)-representation of Γg, we can determine whether this representation is discrete and faithful or not by using 4g-6 explicit trace inequalities. We also show the connectivity and contractibility of Tg from the point of view of SL2(R)-representations of Γg. Previously, these properties of Tg had been proved by using hyperbolic geometry and quasi-conformal deformations of Fuchsian groups. Our method is simple and only uses topological properties of the space of SL2(R)-representations of Γg.

AB - We give a concrete semialgebraic description of Teichmüller space Tg of the closed surface group Γg of genus g(≥2). Our result implies that for any SL2(R)-representation of Γg, we can determine whether this representation is discrete and faithful or not by using 4g-6 explicit trace inequalities. We also show the connectivity and contractibility of Tg from the point of view of SL2(R)-representations of Γg. Previously, these properties of Tg had been proved by using hyperbolic geometry and quasi-conformal deformations of Fuchsian groups. Our method is simple and only uses topological properties of the space of SL2(R)-representations of Γg.

UR - http://www.scopus.com/inward/record.url?scp=25644437257&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=25644437257&partnerID=8YFLogxK

U2 - 10.2977/prims/1195145147

DO - 10.2977/prims/1195145147

M3 - Article

AN - SCOPUS:25644437257

SN - 0034-5318

VL - 33

SP - 527

EP - 571

JO - Publications of the Research Institute for Mathematical Sciences

JF - Publications of the Research Institute for Mathematical Sciences

IS - 4

ER -

Semialgebraic description of Teichmüller space

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this