The interior of discrete projective structures in the Bers fiber

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The space of all projective structures on a closed surface is a holomorphic vector bundle over the Teichmüller space. In this paper, we restrict the space to the Bers fiber over any fixed underlying complex structure and prove that the interior of the set of discrete projective structures in the Bers fiber consists of those having quasifuchsian holonomy.

Original languageEnglish
Pages (from-to)3-12
Number of pages10
JournalAnnales Academiae Scientiarum Fennicae Mathematica
Volume32
Issue number1
Publication statusPublished - 2007
Externally publishedYes

Fingerprint

Projective Structure
Interior
Fiber
Holonomy
Vector Bundle
Complex Structure
Closed

Keywords

  • Bers density conjecture
  • Degenerate group
  • Grafting
  • Holonomy representation
  • Kleinian group
  • Projective structure
  • Quasifuchsian group

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The interior of discrete projective structures in the Bers fiber. / Matsuzaki, Katsuhiko.

In: Annales Academiae Scientiarum Fennicae Mathematica, Vol. 32, No. 1, 2007, p. 3-12.

Research output: Contribution to journalArticle

@article{7dc7f1c268324ac98332bcb9075c4e15,
title = "The interior of discrete projective structures in the Bers fiber",
abstract = "The space of all projective structures on a closed surface is a holomorphic vector bundle over the Teichm{\"u}ller space. In this paper, we restrict the space to the Bers fiber over any fixed underlying complex structure and prove that the interior of the set of discrete projective structures in the Bers fiber consists of those having quasifuchsian holonomy.",
keywords = "Bers density conjecture, Degenerate group, Grafting, Holonomy representation, Kleinian group, Projective structure, Quasifuchsian group",
author = "Katsuhiko Matsuzaki",
year = "2007",
language = "English",
volume = "32",
pages = "3--12",
journal = "Annales Academiae Scientiarum Fennicae Mathematica",
issn = "1239-629X",
publisher = "Finnish Academy of Science and Letters",
number = "1",

}

TY - JOUR

T1 - The interior of discrete projective structures in the Bers fiber

AU - Matsuzaki, Katsuhiko

PY - 2007

Y1 - 2007

N2 - The space of all projective structures on a closed surface is a holomorphic vector bundle over the Teichmüller space. In this paper, we restrict the space to the Bers fiber over any fixed underlying complex structure and prove that the interior of the set of discrete projective structures in the Bers fiber consists of those having quasifuchsian holonomy.

AB - The space of all projective structures on a closed surface is a holomorphic vector bundle over the Teichmüller space. In this paper, we restrict the space to the Bers fiber over any fixed underlying complex structure and prove that the interior of the set of discrete projective structures in the Bers fiber consists of those having quasifuchsian holonomy.

KW - Bers density conjecture

KW - Degenerate group

KW - Grafting

KW - Holonomy representation

KW - Kleinian group

KW - Projective structure

KW - Quasifuchsian group

UR - http://www.scopus.com/inward/record.url?scp=42149159397&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42149159397&partnerID=8YFLogxK

M3 - Article

VL - 32

SP - 3

EP - 12

JO - Annales Academiae Scientiarum Fennicae Mathematica

JF - Annales Academiae Scientiarum Fennicae Mathematica

SN - 1239-629X

IS - 1

ER -