Teichmuller space and its topological dynamics via flat singular metrics on a surface

• Project/Area Number: 23540103
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Josai University
• Principal Investigator: Nishi Haruko 城西大学, 理学部, 准教授 (90274430)
• Co-Investigator(Renkei-kenkyūsha): OHSHIKA Ken'ichi 大阪大学, 大学院理学研究科, 教授 (70183225) ; KOMORI Yohei 早稲田大学, 教育学部, 教授 (70264794) ; MIYACHI Hideki 大阪大学, 大学院理学研究科, 准教授 (40385480)
• Project Period (FY): 2011-04-28 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: タイヒミュラー空間 / 錐状特異点 / 平坦計量 / 擬エルミート計量 / 平坦構造 / 平面多角形

Outline of Final Research Achievements

We study the geometry of Teichmuller space through the identification with the moduli space of flat metrics on a surface with cone singularities and aim to clarify the properties of its topological dynamics. As a result, we obtain the description of the signature of the area form by the cone angle data in the case of Riemann sphere to show the existence of the family of quasi-Hermite metrics on the moduli space of flat metrics with cone singularities of any positive or negative cone angles.

Research Products

• [Int'l Joint Research] Qeensland University(Australia)
• [Journal Article] On the signature of area form on the polygon space (2013)
  • Author(s): Haruko Nishi
  • Journal Title: osai Mathematical Monographs Volume: 6
  • NAID: 120005520763
  • Peer Reviewed
• [Journal Article] A parametrization of Teichmuller space by polygons (2013)
  • Author(s): Haruko Nishi and Ken'ich Ohshika
  • Journal Title: Proceedings of the 7th international conference on nonlinear Analysis and convex analysis-II- (Busan, Korea, 2011) Volume: II
  • Peer Reviewed
• [Journal Article] A parametrisation of Teichmuller space by polygons (2013)
  • Author(s): Haruko Nishi and Ken'ichi Ohshika
  • Journal Title: Proceedings of the 7th International Conference on Nonlinear Analysis and convex Analysis-II-(Busan, Korea, 2011) Volume: II
  • Peer Reviewed
• [Journal Article] On the signature of area form on the polygon space (2013)
  • Author(s): Haruko Nishi
  • Journal Title: Josai Mathematical Monographs Volume: vol.6
  • NAID: 120005520763
  • Peer Reviewed
• [Journal Article] A pseudo-metric on moduli space of hyperelliptic curves (2012)
  • Author(s): Haruko Nishi and Ken'ichi Ohshika
  • Journal Title: Josai Mathematical Monographs Volume: vol.5
  • NAID: 120005520769
  • Peer Reviewed
• [Presentation] Polyhedral structures of the moduli space of configurations of points on P^1 (2016)
  • Author(s): Haruko Nishi
  • Organizer: Geometry and Topology seminar
  • Place of Presentation: Qeensland Univ. (Brisbane, Australia)
  • Year and Date: 2016-02-02
• [Presentation] 球面上のユークリッド錐構造の面積形式の符号について (2014)
  • Author(s): 高山晴子
  • Organizer: リーマン面に関連する位相幾何学
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2014-08-25 – 2014-08-27
  • Invited
• [Presentation] On the signature of area form on the polygon space (2013)
  • Author(s): Haruko Nishi
  • Organizer: The International Conference on Nonlinear Analysis and Optimization
  • Place of Presentation: Kaohsuing, Taiwan
  • Invited
• [Presentation] A pseudo-metric on moduli space of hyperelliptic curves (2012)
  • Author(s): Haruko Nishi
  • Organizer: The 3rd Asian Conference on Nonlinear Analysis and Optimization
  • Place of Presentation: くにびきメッセ（松江）
  • Invited
• [Presentation] A pseudo-metric on moduli space of hyperelliptic curves (2012)
  • Author(s): Haruko Nishi
  • Organizer: Representation theory of algebraic groups and related topics
  • Place of Presentation: 城西大学紀尾井町キャンパス
  • Invited
• [Presentation] A parametrization of Teichmuller space by polygons (2011)
  • Author(s): Haruko Nishi
  • Organizer: NACA2011
  • Place of Presentation: Pukyong National University