Deformation spaces of Kleinian groups and conformal geometry

• Project/Area Number: 19740032
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Nagoya University
• Principal Investigator: ITO Kentaro Nagoya University, 大学院・多元数理科学研究科, 准教授 (00324400)
• Project Period (FY): 2007 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,400,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥600,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000)
• Keywords: クライン群 / 双曲幾何 / 離散群 / リーマン面 / 等角構造 / タイヒミュラー空間

Research Abstract

I studied the boundary behavior of deformation spaces of Kleinian groups. Especially, I obtained a necessary and sufficient condition in which a sequence of punctured torus groups converges/diverges. Therefore we obtained the whole picture of the self-bumping of the space of punctured torus groups. I also revealed the relation between the Maskit slice and the geometric limit of sequences of liner slices when the associated traces tend to 2. I also studied deformation spaces of 4-dimensional Kleinian groups.

Research Products

• [Journal Article] An extension of the Maskit slice for 4-dimensional Kleinian groups (2008)
  • Author(s): Kentaro Ito, Yoshiaki Araki
  • Journal Title: Conform.Geom.Dyn. 12 Pages: 199-226
  • Peer Reviewed
• [Journal Article] On continuous extension of grafting maps (2008)
  • Author(s): Kentaro Ito
  • Journal Title: Trans.Amer.Math.Soc. 360 Pages: 3731-3749
  • Peer Reviewed
• [Journal Article] An extension of the Maskit slice for 4-dimensional Kleinian groups (2008)
  • Author(s): Kentaro Ito, Yoshiaki Araki
  • Journal Title: Conform. Geom. Dyn. 12 Pages: 199-226
  • Peer Reviewed
• [Journal Article] On continuous extension of grafting maps (2008)
  • Author(s): Kentaro Ito
  • Journal Title: Trans. Amer. Math. Soc. 360 Pages: 3731-3749
  • Peer Reviewed
• [Journal Article] An extension of the Maskit slice for 4-dimensional Kleinian groups (2008)
  • Author(s): Kentaro Ito, Yoshiaki Araki
  • Journal Title: Conformal Geometry and Dynanics 12 Pages: 199-229
  • Peer Reviewed
• [Journal Article] Exotic projective structures and quasi-Fuchsian space. II, (2008)
  • Author(s): Kentaro Ito
  • Journal Title: Duke Mathematical Journal 140 Pages: 85-109
  • Peer Reviewed
• [Journal Article] On continuous extensions of grafting maps (2008)
  • Author(s): Kentaro Ito
  • Journal Title: Transaction of American Mathematical Society 360 Pages: 3731-3749
  • Peer Reviewed
• [Journal Article] Exotic projective structures and quasi-Fuchsian space, II (2007)
  • Author(s): Kentaro Ito
  • Journal Title: Duke Math.J. 140 Pages: 85-109
  • Peer Reviewed
• [Journal Article] Exotic projective structures and quasi-Fuchsian space, II (2007)
  • Author(s): Kentaro Ito
  • Journal Title: Duke Math. J. 140 Pages: 85-109
  • Peer Reviewed
• [Presentation] Linear slices and the complex Fenchel-Nielsen coordinate of the punctured torus space (2010)
  • Author(s): 糸健太郎
  • Organizer: 日本数学会2010年度秋季総合分科会函数論分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-22
• [Presentation] Linear slices and the complex Fenchel-Nielsen coordinate of the punctured torus space (2010)
  • Author(s): 糸健太郎
  • Organizer: 日本数学会秋季総合分科会 函数論分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-22
• [Presentation] Linear slices close to a Maskit slice (2010)
  • Author(s): 糸健太郎
  • Organizer: Hyperbolic Geometry and related topics
  • Place of Presentation: Korean Institute of Advanced Science.
  • Year and Date: 2010-09-15
• [Presentation] Linear slices close to a Maskit slice (2010)
  • Author(s): 糸健太郎
  • Organizer: Hyperbolic Geometry and related topics
  • Place of Presentation: KIAS
  • Year and Date: 2010-09-15
• [Presentation] Linear slices close to a Maskit slice (2010)
  • Author(s): 糸健太郎
  • Organizer: Workshop on Geometry, Topology and Dynamics of Character Varieties
  • Place of Presentation: National University of Singapore.
  • Year and Date: 2010-07-30
• [Presentation] Linear slices close to a Maskit slice (2010)
  • Author(s): 糸健太郎
  • Organizer: Geometry, Topology and Dynamics of Character Varieties
  • Place of Presentation: National University of Singapore
  • Year and Date: 2010-07-30
• [Presentation] Linear slices close to a Maskit slice (2010)
  • Author(s): 糸健太郎
  • Organizer: 日本数学会2010年度年会函数論分科会
  • Place of Presentation: 慶応大学
  • Year and Date: 2010-03-24
• [Presentation] Linear Slices close to a Maskit slice (2010)
  • Author(s): 糸健太郎
  • Organizer: 日本数学会2010年度年会 函数論分科会
  • Place of Presentation: 慶応大学
  • Year and Date: 2010-03-24
• [Presentation] Linear slices of Kleinianpunctured torus space close to aMaskit slice (2010)
  • Author(s): 糸健太郎
  • Organizer: 「リーマン面・不連続群」研究集会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-01-09
• [Presentation] Linear slices of Kleinian punctured torus space close to a Maskit slice (2010)
  • Author(s): 糸健太郎
  • Organizer: 「リーマン面・不連続群」研究集会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-01-09
• [Presentation] 穴あきトーラス群の擬フックス群空間について (2008)
  • Author(s): 糸健太郎
  • Organizer: 日本数学会2008年度秋季総合分科会函数論分科会特別講演
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] 穴あきトーラスの擬フックス空間について (2008)
  • Author(s): 糸健太郎
  • Organizer: 日本数学会2008年度秋季総合分科会函数論分科会特別講演
  • Place of Presentation: 東京工業大学
  • Year and Date: 2008-09-24
• [Presentation] Topology of quasifuchsian space of once-punctured torus (2007)
  • Author(s): 糸健太郎
  • Organizer: Workshop on infinite dimensional Teichmuller space and moduli space
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2007-11-21
• [Presentation] Topology of quasifuchsian space of once-punctured torus (2007)
  • Author(s): Kentaro Ito
  • Organizer: Workshop on infinite dimensional Teichm〓uller space and moduli space
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2007-11-21
• [Remarks] ホームページ等
  • URL: http://www.math.nagoya-u.ac.jp/~itoken/index.html
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