1993 Fiscal Year Annual Research Report

曲面の写像類群と3次元多様体の研究

Research Project

Project/Area Number	05640088
Research Institution	University of Tsukuba
Principal Investigator	金戸武司筑波大学, 数学系, 講師 (70107340)
Co-Investigator(Kenkyū-buntansha)	江田勝哉筑波大学, 数学系, 助教授 (90015826) 星野光男筑波大学, 数学系, 助手 (90181495) 増田哲也筑波大学, 数学系, 講師 (70202314) 相山玲子筑波大学, 数学系, 助手 (20222466) 酒井克郎筑波大学, 数学系, 講師 (50036084)
Keywords	曲面 / 自己同相写像 / 写像類群 / 双曲的構造 / 3次元多様体 / Heegaard分解
Research Abstract	研究代表者及び分担者は曲面の写像類群の研究を通して3次元多様体の位相的性質を明らかにするため,特に曲面上の同相写像を円周S^1上の同相写像に帰着させるNielsen-Thurstonのideaに基づき,交付申請書の研究目的・実施計画に沿って研究を進め以下の成果を得た。 1.研究目的(1)について。種数2以上の曲面Σ上の双曲的普遍被覆写像P:1H^2→Σの被覆変換群Γは,1H^2(双曲平面)を単位円板モデルとするとき,単位円周S^1上にも作用しているとみなせる。このとき,S^1上の同相写像fがΣ上の同相写像に対応するための必要十分条件はf^<-1>Γf=Γである。 2.研究目的(2)について。Σ上の双曲的構造を定めるΓ及びP:1H^2→γに関し,正多角形を基本領域とするもので,従来知られているΓと異なり,多くの良い対称性をもつΓを発見した。これは研究目的(2)の方向での今後の研究に大いに寄与することが期待できる。 3.研究目的(3)について。VをΣを境界にもつ3次元ハンドル体とする。V上の同相写像は境界Σ上の同相写像を引き起し,更にS^1上の同相写像に対応する。逆はそれぞれの段階で一般には対応しない。S^1上の同相写像がV上の同相写像に対応するための必要十分条件を上記1と類似の形で得た。これは研究目的(3)を進める上で重要な役割を果す基本的な結果である。代表者金戸は上記1,2,3の主要部分に,分担者はそれぞれの専門を活した役割分担に基づき,主として,中川,保科,酒井,横井,宮下,増田,笠井,星野,柴田は1に,相山は2に,高橋は3に,本橋,江田,坪井,塚田は研究目的遂行の戦略にそれぞれ側面から有益な貢献をした。又,各分担者はこの研究に関連して,それぞれの専門分野における多くの研究成果(11.研究発表欄(裏面)参照)を得た。

Research Products
(21 results)

All Other

All Publications (21 results)

[Publications] Bao-Lin Guo(酒井克郎と共著): "Hyperspaces of CW-comlexes" Fund.Math.143. 23-40 (1993)
[Publications] Katsuro Sakai: "A Q^∞-manifold topdogy of the space of Lipschitz maps" Topology Appl.53. 7-18 (1993)
[Publications] Nguyan To Nhu(酒井克郎と共著): "The compact neighborhood extension property and local equi-connectedness" Proc.Amer.Math.Soc.(in press).
[Publications] Katsuro Sakai: "All autohomeomorphisms of connected Menger manifolds are stable" Proc.Amer.Math.Soc.(to appear).
[Publications] Katsuro Sakai: "Free actions of zero-dimensional compact groups on Menger manifolds" Proc.Amer.Math.Soc.(in press).
[Publications] Akira Koyama(横井勝弥と共著): "A unified approach of characterizations and resolutions for cohomological dimension modulo P" Tsukuba J.Math.(to appear).
[Publications] Reiko Aiyama: "The generalized Gauss map of a space-like submanifold with parallel mean curvature vector in a pseudo-Euclidean space" Japanese J.Math.20(No.1)(to appear). (1994)
[Publications] Reiko Aiyama: "Compact space-like m-submanifolds in a pseudo-Riemennias sphere S^<m+p>_p(C)" Tokyo Journal Math.18(No.1)(to appear).
[Publications] Tetsuya Masuda(共著): "A von Neu mann algebra frame work for the duality of the quantum groups" Publ.RIMS Kyoto Univ.(to appear).
[Publications] Tomoyuki Kakei(増田哲也と共著): "Spectrum of an operator appears in the quantum SU(II) group" Quantum and Non-commutative analysis,Math.Phys.studies(Kluwer Academic Publishers). 16. 253-261 (1993)
[Publications] Tetsuya Masuda(共著): "Algebras of guantum groups as quantized Poisson manifolds" Proc.of the Workshop on Geometry and its Appl.(World Scientific). 109-120 (1993)
[Publications] Mitsuo Hoshino: "Noetherian rings of self-injective dimension two" Comm.Algera. 21. 1071-1094 (1993)
[Publications] Hideto Asashiba(星野光男と共著): "Bilinea maps which define local algebras with trivial Hochschild cohomology" Canad.Math.Soc.Conf.Proc.14. 15-28 (1993)
[Publications] Mitsuo Hoshino: "Vanishing of Hochchild cohomologies for local rings with embedding dimension two" Canad.Math.Bull.(to appear).
[Publications] Katsuya Eda(共著): "Abelian groups of continuous functions and their duals" Topology Appl.53. 131-151 (1993)
[Publications] Katsuya Eda(共著): "Prime spaces in free topological groups" Topology Appl.(to appear).
[Publications] Katsuya Eda(共著): "The Dugundji extension theorem and extension degree" Coll.Math.(to appear).
[Publications] Moto-o Takahashi: "Non-triviality of certain finitely presented groups" Tsukuba J.Math. (to appear).
[Publications] Akito Tsuboi: "Large indiscernible sets of a structure" Kobe J.Math.10. 173-178 (1993)
[Publications] Hirotaka Kikyo(坪井明人と共著): "On reduction properties" J.Symbolic Logic. (to appear).
[Publications] Nobutaka Tsukada: "Constructions of complete metric spaces and compact Hausdorff spaces which are not Baire spaces" Tsukuba J.Math.17. 159-167 (1993)

1993 Fiscal Year Annual Research Report

曲面の写像類群と3次元多様体の研究

Principal Investigator

金戸 武司 筑波大学, 数学系, 講師 (70107340)

Research Products

[Publications] Bao-Lin Guo(酒井克郎と共著): "Hyperspaces of CW-comlexes" Fund.Math.143. 23-40 (1993)

[Publications] Katsuro Sakai: "A Q^∞-manifold topdogy of the space of Lipschitz maps" Topology Appl.53. 7-18 (1993)

[Publications] Nguyan To Nhu(酒井克郎と共著): "The compact neighborhood extension property and local equi-connectedness" Proc.Amer.Math.Soc.(in press).

[Publications] Katsuro Sakai: "All autohomeomorphisms of connected Menger manifolds are stable" Proc.Amer.Math.Soc.(to appear).

[Publications] Katsuro Sakai: "Free actions of zero-dimensional compact groups on Menger manifolds" Proc.Amer.Math.Soc.(in press).

[Publications] Akira Koyama(横井勝弥と共著): "A unified approach of characterizations and resolutions for cohomological dimension modulo P" Tsukuba J.Math.(to appear).

[Publications] Reiko Aiyama: "The generalized Gauss map of a space-like submanifold with parallel mean curvature vector in a pseudo-Euclidean space" Japanese J.Math.20(No.1)(to appear). (1994)

[Publications] Reiko Aiyama: "Compact space-like m-submanifolds in a pseudo-Riemennias sphere S^<m+p>_p(C)" Tokyo Journal Math.18(No.1)(to appear).

[Publications] Tetsuya Masuda(共著): "A von Neu mann algebra frame work for the duality of the quantum groups" Publ.RIMS Kyoto Univ.(to appear).

[Publications] Tomoyuki Kakei(増田哲也と共著): "Spectrum of an operator appears in the quantum SU(II) group" Quantum and Non-commutative analysis,Math.Phys.studies(Kluwer Academic Publishers). 16. 253-261 (1993)

[Publications] Tetsuya Masuda(共著): "Algebras of guantum groups as quantized Poisson manifolds" Proc.of the Workshop on Geometry and its Appl.(World Scientific). 109-120 (1993)

[Publications] Mitsuo Hoshino: "Noetherian rings of self-injective dimension two" Comm.Algera. 21. 1071-1094 (1993)

[Publications] Hideto Asashiba(星野光男と共著): "Bilinea maps which define local algebras with trivial Hochschild cohomology" Canad.Math.Soc.Conf.Proc.14. 15-28 (1993)

[Publications] Mitsuo Hoshino: "Vanishing of Hochchild cohomologies for local rings with embedding dimension two" Canad.Math.Bull.(to appear).

[Publications] Katsuya Eda(共著): "Abelian groups of continuous functions and their duals" Topology Appl.53. 131-151 (1993)

[Publications] Katsuya Eda(共著): "Prime spaces in free topological groups" Topology Appl.(to appear).

[Publications] Katsuya Eda(共著): "The Dugundji extension theorem and extension degree" Coll.Math.(to appear).

[Publications] Moto-o Takahashi: "Non-triviality of certain finitely presented groups" Tsukuba J.Math. (to appear).

[Publications] Akito Tsuboi: "Large indiscernible sets of a structure" Kobe J.Math.10. 173-178 (1993)

[Publications] Hirotaka Kikyo(坪井明人と共著): "On reduction properties" J.Symbolic Logic. (to appear).

[Publications] Nobutaka Tsukada: "Constructions of complete metric spaces and compact Hausdorff spaces which are not Baire spaces" Tsukuba J.Math.17. 159-167 (1993)

金戸武司筑波大学, 数学系, 講師 (70107340)