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リーマン面の正則族のモノドロミーの大域的研究

Research Project

Project/Area Number 13874025
Research Category

Grant-in-Aid for Exploratory Research

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionOsaka City University

Principal Investigator

今吉 洋一  大阪市立大学, 大学院・理学研究科, 教授 (30091656)

Co-Investigator(Kenkyū-buntansha) 佐官 謙一  大阪市立大学, 大学院・理学研究科, 助教授 (70110856)
釜江 哲朗  大阪市立大学, 大学院・理学研究科, 教授 (80047258)
河内 明夫  大阪市立大学, 大学院・理学研究科, 教授 (00112524)
加藤 信  大阪市立大学, 大学院・理学研究科, 助教授 (10243354)
西尾 昌治  大阪市立大学, 大学院・理学研究科, 助教授 (90228156)
帰山 奨  大阪市立大学, 大学院・理学研究科, 講師 (60047206)
Project Period (FY) 2001 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2003: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2002: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Keywordsリーマン面 / 正則族 / モノドロミー / 写像類群 / タイヒミュラー空間 / 普遍被覆空間 / Riemann surface / Teichmiiller space / monodromy / mapping clap group / complex mainfold / universal covering / uniformization / quasi comformal mapping
Research Abstract

リーマン面の正則族のモノドロミーの大域的な研究に関連して、研究代表者は次のような研究成果を得た。
(1)解析的有限な(g, n)型の双曲的リーマン面Sに対して、2元複素多様体B={(x, y)∈S×S|x≠y},3元複素多様体M={(x, y, z)∈S×S×S|x≠y, y≠z, z≠x},および射影π:M→Bを考えれば、B上の(g, n+2)型のリーマン面の正則族(M,π,B)が得られる。この正則族のモノドロミーのタイプをBersとThurstonによる方法で完全に分類することができた。この研究成果はOsaka J. Math.から出版された。
(2)上の(1)の結果を一般の次元に拡張することができた。これに関する論文は、Journal of Knot Theory and Its Ramificationsに掲載されることが決まっている。
(3)リーマン面の正則族(M,π,S)に対して。2次元複素多様体Mの普遍被覆空間M^^〜の形を決定する問題を考察した。主結果としては,(i)M^^〜は強擬凸領域と双正則同値にならない、(ii)M^^〜は一般には多重円板と双正則同値にならず,また多重円板と双正則同値になるための必要十分条件も与えたことが挙げられる。この成果はKodai Math. J.に投稿中である。
(4)負型の擬周期写像が任意に与えられたとき、それをモノドロミーを持つ穴開き単位円板Δ^*={0<|t|<1}上のリーマン面の正則族(M,π,Δ^*)を構成する問題を考察した。構成できることはMatsumotoとMontesinosによって証明されているが、そのようなもの全部を統一的に構成する方法が得られた。

Report

(3 results)
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (25 results)

All Other

All Publications (25 results)

  • [Publications] Yoichi Imayoshi: "On the Nielsen-Thurston-Bers type of some selfmaps of Riemann surfaces with two specified points"Osaka J. of Math.. 40巻2号. 659-685 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Yoichi Imayoshi: "A reducibility problem for monodromy of some surface bundles"Journal of Knot Theory and Its Ramifications. (掲載予定).

    • Related Report
      2003 Annual Research Report
  • [Publications] Akio Kawauchi: "On linking signature invariants of surface-knots"Journal of Knot Theory and Its Ramifications. 11. 369-385 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] Akio Kawauchi: "On pseudo-ribbon surface-links"Journal of Knot Theory and Its Ramifications. 11. 1043-1062 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] Akio Kawauchi: "An intrinsic Arf invariant of a link and its surface-link analogue"Proc. of the first topology meeting of Japan-Mexico 1999,Topology Appl. 121. 255-274 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] Ken-ichi Sakan: "On pseudo-metrics on the space of generalized quasisymmetric automorphisms of a Jordan curve"Ann. Univ. Mariae Curie-Sklodowska. Sect. A 55. 115-138 (2001)

    • Related Report
      2003 Annual Research Report
  • [Publications] Masaharu Nishio: "A characterization of caloric morphisms between manifolds"Ann.Acad.Sci.Fenn.Math.. (掲載予定).

    • Related Report
      2003 Annual Research Report
  • [Publications] Shin Kato: "General existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux"Comm.Anal.Geom.. 8. 83-114 (2000)

    • Related Report
      2003 Annual Research Report
  • [Publications] Yohei Komori: "On the boundary of the Earle slice for punctured torus groups, Kleinian groups and hyperbolic 3-manifolds"Lond.Math.Soc.Lec.Notes. 299. 293-304 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Tetsro Kamae: "Sequence entropy and maximal pattern complexity of infinite words"Ergodic Theory and Dynamical Systems. (掲載予定).

    • Related Report
      2003 Annual Research Report
  • [Publications] Tetsro Kamae: "Maximal pattern complexity for discrete systems"Ergodic Theory and Dynamical Systems. (掲載予定).

    • Related Report
      2003 Annual Research Report
  • [Publications] Y.Imayoshi, M.Ito, H.Yamamoto: "A remark on the Bers type of some self-maps of Riemann surface with two specified points"Proc. of the Second ISSAC Congress, International Society for Analysis, Applications and Computation. 8. 871-875 (2000)

    • Related Report
      2002 Annual Research Report
  • [Publications] Y.Imayoshi, M.Ito, H.Yamamoto: "The Nielsen-Tharston-Bers type of elements of the monodromy group of a holomorphic family of Riemann surfaces"Lecture Motes in Pure and Applied Mathematics. 214. 169-177 (2000)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Kawauchi: "Algelraic characterizaton of an exact 4-manifold with infinits cyclis first homology"Atti. Sem. Mat. Fis. Unis.. to appear.

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Kato, M.Umehara, K.Yamada: "General existence of minimal surfaces of genes zers with catenoidal ends and presciefed flux"Comm. Anal. Geom.. 8. 83-114 (2000)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Sakan, D.Partyka: "On pseudo-metrics on the space of generalized quosisymmetric automirphisms of a Jordan curve"Aun. Univ. Marie Curie-Sklodowaka. A55. 115-138 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Nishio, K.Shimomura: "A characterization of caloric morpkisms between monifolds"Ann. Acad. Sci. Fenn. Math.. to appear.

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Needham(今吉洋一他訳): "ヴィジュアル複素解析"培風館. 662 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Yoichi Imayoshi: "A remark on the Bers type of some self-mapws of Riemann surfaces with two specified points"Proc. of the Second ISSAC Congress, International Society for Analysis, Applications and Computation. 8. 871-875 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Yoichi Imayoshi: "The Nielsen-Bers type of elements of the monodromy group of a Holomorphic family of Riemann surfaces induced by a Kodaira surface"Lecture Notes in Pure and Applied Mathematics. 214. 169-177 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Akio Kawauchi: "Algebraic characterization of an exact 4-manifold with infinite cyclic first homology"Atti.Sem.Mat.Fis.Univ.. (発表予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] Kenichi Sakan: "A conformally invariant dilatation of quasisymmetry"Ann. Univ. Mariae Curie-Sklodowska Sect.A. 3. 167-181 (1999)

    • Related Report
      2001 Annual Research Report
  • [Publications] Shin Kato: "General existence of minimal surfaces of genus zero with catenoidal ends and prescribed flux,Communications in Analysis and Geometry"Comm. Anal. Geo.. 8. 83-114 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kenichi Sakan: "On pseudo-metrics on the space of generalized quasisymmetric automorphisms of a Jordan curve"Ann. Univ. Mariae Curie-Sklodowska Sect. A. 55. 115-138 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.ニーダム(今吉洋一他訳): "ヴィジュアル複素解析"培風館. 662 (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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