Fixed point theorems and cobordism

不动点定理和配边

• 批准号: 05452008
• 负责人: KAWAKUBO Katsuo
• 金额: $ 2.62万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05452008/
• 关键词: Fixed point theorems; Cobordism; Homotopy representation; Burnside ring; Knot; Hecke algebra; Lefschetz ring; Alexander polynomial; コンパクト・リー群; G-sコボルディズム; G同相; Lefachety環; 誘導準同型; 制限準同型; 線型表現; モジュライ空間; Lefschetz環; 埋め込み; Whitehead群

Kawakubo constructed G-manifolds which are G-s-cobordant, but are not G-homeomorphic for arbitrary compact Lie groups G.Nagasaki computed the structure of the LH groups which are introduced for the purpose of investigating the linearity of homotopy representations of finite groups. As an application, he determined the set of finite groups whose homotopy representations are always linear. Murakami constructed a vertex type state model in Turaev's sense for the multi-variable Alexander polynomial. By using this model, a new set of axioms for the multi-variable Alexander polynomial is obtained. He also determined the structure of the centralizer algebra of the mixed tensor representations of the quantum group U_q (gl (n, c) ). This algebra can be considered as a generalization of the Iwahori Hecke algebra of type A.Using this algebra, he generalized the Yamada polynomial, which is an invariant of embeddings of a spatial graph in S^3. He also investigated representations of the category of tangles using Kontsevich's iterated integral, and succeeded in giving a combinatorial description of Kontsevich's integrals of knots, links and tangles.

Kawakubo构造了G-流形是G-s-协边的，但不是G-同胚的任意紧李群G.长崎计算了LH群的结构，这些LH群是为了研究有限群的同伦表示的线性性而引入的。作为一个应用，他确定了一套有限群的同伦表示总是线性的。Murakami为多元亚历山大多项式构造了Turaev意义下的顶点型状态模型。利用该模型，得到了多元亚历山大多项式的一组新公理。他还确定了结构的中心化代数的混合张量表示的量子群U_q（gl（n，c））。这个代数可以被认为是A型Iwahori Hecke代数的推广。使用这个代数，他推广了山田多项式，这是空间图在S^3中嵌入的不变量。他还调查表示类别的缠结使用Kontsevich的迭代积分，并成功地给出了组合描述Kontsevich的积分的结，链接和缠结。

项目成果

宮西正宜: "開代数曲面の最近の話題" 数学. 46-3. 243-257 (1994)

Masayoshi Miyanishi：“开放代数曲面的最新主题”，数学 46-3。

K.Kawakubo: "G-S-cobordant manifolds are not neclssarlly G-homeomorphic for arbit ary compact Lie groups G" Journal of the Mathoematical Society of Japan. 45. 599-610 (1993)

K.Kawakubo：“对于任意紧李群 G，G-S 协调流形不一定是 G 同胚”，日本数学会杂志。

J.MURAKAMI: "The Yamada polynomial of spacial graphs and knit algebra" Communications in Mathematical Physics. 155. 511-522 (1993)

J.MURAKAMI：“空间图和针织代数的山田多项式”数学物理通讯。

K.KAWAKUBO: "G-s-cobordant manifolds are not necessarily G-homeomorphic for arbitrary compact Lie groups G" Journal of the Mathematical Society of Japan. 45. 599-610 (1993)

K.KAWAKUBO：“对于任意紧李群 G，G-s-协配流形不一定是 G-同胚”日本数学会杂志。

M.Miyanishi: "Vector fields on factorial schemes" J.Algebra. 172(to appear). (1995)

M.Miyanishi：“阶乘方案上的向量场”J.Algebra。