1998 Fiscal Year Final Research Report Summary

ヘガード分解と基本群の3組

Research Project

Project/Area Number	09640087
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Geometry
Research Institution	University of Tsukuba
Principal Investigator	金戸武石筑波大学, 数学系, 講師 (70107340)
Co-Investigator(Kenkyū-buntansha)	川村一宏筑波大学, 数学系, 講師 (40204771) 酒井克郎筑波大学, 数学系, 助教授 (50036084) 加藤久男筑波大学, 数学系, 教授 (70152733) 山形邦夫東京農工大学, 工学部, 教授 (60015849) 芥川玲子 (相山玲子) 筑波大学, 数学系, 助手 (20222466)
Project Period (FY)	1997 – 1998
Keywords	ヘガード分解 / ヘガードダイアグラム / 3次元多様態 / 基本群 / リンク / ブラケット / 曲面 / 厚み付き曲面
Research Abstract	3次元多様体へのヘガード分解に対応する、ヘガード曲面Σの基本群Gとその2つの正規部分群G_1,G_2の3組によりヘガード分解及び3次元多様体の位相的性質の研究を目的とし、以下を得た。 1.統計力学的手法による研究:ヘガードダイアグラムをヘガード曲面Σの上のリンクダイアグラムとみなすことによりΣxRにおけるリンク理論と密接な関連を持つ。実際、これまでの研究で有向リンクL(⊂ΣxR)のアンビィエントイソトピー不変量として、Σ内の余次元1のリンクで生成されるZ[A, A^<-1>]係数の自由加群∧(Σ)に値をもつFL(A)をどうにゅうし種類1のヘガード分解をもつ3次元多用体のクラスに対する位相不変量を得ている。この方向での研究の基礎として、ΣxR内のリンクについて、(1)ΣxR上の自己同相によるリンクの同値不変量(2)分離可能リンクに関する積定理(3)電気回路網における電気伝導率に由来するアイデアを発展させ、無向リンクに対する分数多項式型のアンビィエントイソトピー不変量(4)交代リンクに対するテイト型定理(5)「どんなG_1∩G_2が単純閉曲線の非自明なホモトピー類を含むか」について、自然な写像ψ:G→∧(Σ)による像の単項性(「ジョーンズ多項式1の結び目は自明か」とも関連)を調べることが有効である等の結果を得た。 2.双曲幾何の手法による研究:種数2以上のヘガード曲面Σについて、Σ上の双曲的構造H^2/Г(H^2:双曲平面Г:PSL(2,R)の離散部分群により3組(G;G_1,G_2)はГとその2つの正規部分群による3組(Г;Г_1、Г_2)に対応する。これについて、従来とは異なり多くの対称性をもつГの新しい生成系が具体的に2x2行列として得られた。これにより、ヘガードダイアグラムからГ_1、Г_2の「生成系」も効率的に得られる。 3.分担者の専門とする手法による研究:各分担者は本研究と関連する基礎研究として興味深い多くの成果を得た。

Research Products

(21 results)

All Other

All Publications (21 results)

[Publications] Hisao Kato: "The nonexistence of expansive homeomorphisms of continua which contains all decomposable circle-like continua"Trans. Amer. Math. Soc.. 345. 3645-3655 (1997)
[Publications] Hisao Kato: "A note on expansive homeomorphisms on surfaces with holes"Topology and its Appl.. 82. 267-277 (1998)
[Publications] Hisao Kato: "Indecomposability of chaotic continua on surfaces"Bull. Polish Acad. Scil, Math.. 46. 2151-2157 (1998)
[Publications] Katsuro Sakai: "Semi-free actions of zero-dimensional compact groups on Menger manifolds"Proc. Amer. Math. Soc.. 125. 2809-2813 (1997)
[Publications] Katsuro Sakai et al.: "A Q-manifold compactification of the homeomorphism group of a graph"Bull. Polish Acad. Scil, Math.. 45. 281-286 (1997)
[Publications] Katsuro Sakai: "Proper n-shape categories"Glasnik Math.. (印刷中).
[Publications] Kazuhiro Kawamura et al.: "Universal spaces for a class of Lasnev spaces"Topology and its Appl.. 85. 175-193 (1998)
[Publications] Kazuhiro Kawamura et al.: "Total excess and Tits metric for piecewise Riemannian 2-manifolds"Topology and its Appl.. (To appear).
[Publications] Kazuhiro Kawamura et al.: "The existence of a straight line of piecewise Riemannian 2-manifolds"Note Di Matematica. (To appear).
[Publications] Reiko Aiyama et al.: "Kenmotsu-Bryant type representation formula for constant mean curvature spacelike surfaces in (・c)"Diff. Geom. Its Appl.. 9. 251-272 (1998)
[Publications] Reiko Aiyama et al.: "Kenmotsu-Bryant type representation formula for constant mean curvature spacelike surfaces in (・c) and (c)"Ann. Global Anal. Geom.. 17. 49-75 (1998)
[Publications] A. Skowronski & Kunio Yamagata: "Stable equivalence of selfinjective algebras of titled type"Archive der Mathematik. 70. 341-350 (1998)
[Publications] A. Skowronski & Kunio Yamagata: "Galois coverings of selfinjective algebras by repetitive algebras"Trans. Amer. Math. Soc.. (印刷中).
[Publications] Takao Hoshina & Kaori Yamazaki: "Extensions of junctions on product spaces"Topology and its Appl.. 82. 195-204 (1998)
[Publications] Katsuya Yokoi: "Localization in deimension theory"Topology and its Appl.. 84. 268-281 (1998)
[Publications] Katsuya Yokoi: "On the shape asphericity of compacta"Bull. Polish Acad. Sci., Math.. 46. 249-264 (1998)
[Publications] Kaori Yamazaki: "Normality and collectionwise normality of product spaces II"Tsukuba J. Math.. 22. 783-793 (1998)
[Publications] Mitsuhiro Itoh: "Automorphisms and Conjugate connections"Hokkaido Math. J.. 26. 141-155 (1997)
[Publications] Mitsuhiro Itoh: "Odd-dimensional Tori and Contact structure"Proc. Japan Acad.. 73. 58-59 (1997)
[Publications] Mituhiro Itoh: "Compact Einstein-Weyl Manfifolds and The associated Constants"Osaka J. Math.. 35. 567-578 (1998)
[Publications] Hiroyuki Tasaki: "The group of tangent vectors to a Lie group and the differential of its exponential mapping"Kyungpllk Math. J.. 38. 205-209 (1998)

1998 Fiscal Year Final Research Report Summary

ヘガード分解と基本群の3組

Principal Investigator

金戸 武石 筑波大学, 数学系, 講師 (70107340)

Research Products

[Publications] Hisao Kato: "The nonexistence of expansive homeomorphisms of continua which contains all decomposable circle-like continua"Trans. Amer. Math. Soc.. 345. 3645-3655 (1997)

[Publications] Hisao Kato: "A note on expansive homeomorphisms on surfaces with holes"Topology and its Appl.. 82. 267-277 (1998)

[Publications] Hisao Kato: "Indecomposability of chaotic continua on surfaces"Bull. Polish Acad. Scil, Math.. 46. 2151-2157 (1998)

[Publications] Katsuro Sakai: "Semi-free actions of zero-dimensional compact groups on Menger manifolds"Proc. Amer. Math. Soc.. 125. 2809-2813 (1997)

[Publications] Katsuro Sakai et al.: "A Q-manifold compactification of the homeomorphism group of a graph"Bull. Polish Acad. Scil, Math.. 45. 281-286 (1997)

[Publications] Katsuro Sakai: "Proper n-shape categories"Glasnik Math.. (印刷中).

[Publications] Kazuhiro Kawamura et al.: "Universal spaces for a class of Lasnev spaces"Topology and its Appl.. 85. 175-193 (1998)

[Publications] Kazuhiro Kawamura et al.: "Total excess and Tits metric for piecewise Riemannian 2-manifolds"Topology and its Appl.. (To appear).

[Publications] Kazuhiro Kawamura et al.: "The existence of a straight line of piecewise Riemannian 2-manifolds"Note Di Matematica. (To appear).

[Publications] Reiko Aiyama et al.: "Kenmotsu-Bryant type representation formula for constant mean curvature spacelike surfaces in (・c)"Diff. Geom. Its Appl.. 9. 251-272 (1998)

[Publications] Reiko Aiyama et al.: "Kenmotsu-Bryant type representation formula for constant mean curvature spacelike surfaces in (・c) and (c)"Ann. Global Anal. Geom.. 17. 49-75 (1998)

[Publications] A. Skowronski & Kunio Yamagata: "Stable equivalence of selfinjective algebras of titled type"Archive der Mathematik. 70. 341-350 (1998)

[Publications] A. Skowronski & Kunio Yamagata: "Galois coverings of selfinjective algebras by repetitive algebras"Trans. Amer. Math. Soc.. (印刷中).

[Publications] Takao Hoshina & Kaori Yamazaki: "Extensions of junctions on product spaces"Topology and its Appl.. 82. 195-204 (1998)

[Publications] Katsuya Yokoi: "Localization in deimension theory"Topology and its Appl.. 84. 268-281 (1998)

[Publications] Katsuya Yokoi: "On the shape asphericity of compacta"Bull. Polish Acad. Sci., Math.. 46. 249-264 (1998)

[Publications] Kaori Yamazaki: "Normality and collectionwise normality of product spaces II"Tsukuba J. Math.. 22. 783-793 (1998)

[Publications] Mitsuhiro Itoh: "Automorphisms and Conjugate connections"Hokkaido Math. J.. 26. 141-155 (1997)

[Publications] Mitsuhiro Itoh: "Odd-dimensional Tori and Contact structure"Proc. Japan Acad.. 73. 58-59 (1997)

[Publications] Mituhiro Itoh: "Compact Einstein-Weyl Manfifolds and The associated Constants"Osaka J. Math.. 35. 567-578 (1998)

[Publications] Hiroyuki Tasaki: "The group of tangent vectors to a Lie group and the differential of its exponential mapping"Kyungpllk Math. J.. 38. 205-209 (1998)

金戸武石筑波大学, 数学系, 講師 (70107340)