3次元多様体及びそれに含まれる結び目,絡み目,グラフの研究

2000 Fiscal Year Annual Research Report

• Project/Area Number: 12640091
• Research Institution: Tokyo Woman's Christian University
• Principal Investigator: 小林 一章 東京女子大学, 文理学部, 教授 (50031323)
• Co-Investigator(Kenkyū-buntansha): 宮地 晶彦 東京女子大学, 文理学部, 教授 (60107696) ; 近藤 武 東京女子大学, 文理学部, 教授 (20012338) ; 谷山 公規 東京女子大学, 文理学部, 助教授 (10247207) ; 石渡 万希子 東京女子大学, 文理学部, 助手 (80277095) ; 大阿久 俊則 東京女子大学, 文理学部, 教授 (60152039)
• Keywords: boundary link / ribbon link / Vassiliev invariant / spatial graph / homology sphere / Moonshine VOA / Hardy space / D-module

Research Abstract

3次元多様体自身の研究及び3次元多様体に含まれる結び目,絡み目,グラフの研究を行ない,数回の研究集会及び研究連絡を行なった.高い分離性をもつ絡み目のうち,free h-trivial link(strong h-trivial link),boundary link,h-split link,separate ribbou linkについてその差異を調べた.又3次元球面に含まれる空間グラフの中の結び目のVassiliev不変量等を調べ,位相空間を互いに交わらなく,かつ同相なものに分ける事も調べた.また3次元多様体自身の研究としてはZ-ホモロジ-球面がどのようなAlexander多項式をもち,どのような種類の絡み目を手術する事により得られるかを研究した.更にDS-diagsamの拡張として境界つきDS-diagsamの定義を決定し,応用範囲を広げた.

Research Products

• [Publications] Kazuaki Kobayashi: "Boundary links which are not homotopically split"Kobe Journal of Mathematics . 17巻1号. 59-69 (2000)
• [Publications] Kazuaki Kobayashi: "Ribbon links and separate ribbon links"Hakone Seminar 2000. (to appear). (2001)
• [Publications] Kouki Taniyama: "Higer dimensional links in a simplicial complex embedded in a sphere"Pacific Journal of Mathematics. 194巻2号. 465-467 (2000)
• [Publications] Kouki Taniyama(with Yoshiuki Ohyama): "Vassiliev invariants of knots in a spatial graph"Pacific Journal of Mathematics. (to appear).
• [Publications] Kouki Taniyama: "Dividing a topological space into mutually disjoint and mutually homeomorphic subspaceDviding a topalogical space into mutually disjoint and mutually homeomorphic subspace"Topology and its applications. (to appear).
• [Publications] Makiko Ishiwata: "A surgery description of an integral homology three sphere respecting the Casson int."Journal of knot theory and its ramifications. (to appear).
• [Publications] Takeshi Kondo: "The calculation of the character of Mooshine VOA"Advanced Study in pure mathematics. (to appear).
• [Publications] Akihiko Miyachi: "Hardy space estimate for the product of singular integrals"Canadian Journal of Mathematics. 52巻2号. 381-411 (2000)
• [Publications] Akihiko Miyachi: "Remarks on Herz Type Hardy spaces"Acta Mathematica Sinica (English Ser.). 17巻2号(to appear). (2000)
• [Publications] Toshinori Oaku: "A localization algorithm for D-modules"J.Symbolic Computation. 29巻. 721-728 (2000)
• [Publications] Toshinori Oaku: "Algorithms for D-modules-restriction,tensor product,localization and local cohomology groups"Jourrnal of Pure and Applied Algebra. 156巻. 267-308 (2001)
• [Publications] Toshinori Oaku: "Polynomial and rational solutions of holonomic systems"Journal of Pure and Applied Algebra. (to appear).
• [Publications] 大阿久俊則(with高山信毅): "D加群の極小自由分解"京都大学数理解析研究所講究録. 1171巻. 128-155 (2000)