Homotopy noncommutativity of loop spaces

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400087
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: Kishimoto Daisuke 京都大学, 理学(系)研究科(研究院), 准教授 (60402765)
• Co-Investigator(Renkei-kenkyūsha): KONO Akira 同志社大学, 理工学部, 教授 (00093237) ; IRIYE Kouyemon 大阪府立大学, 大学院理学研究科, 教授 (40151691) ; IWASE Norio 九州大学, 大学院数理学研究院, 教授 (60213287) ; KURIBAYASHI Katsuhiko 信州大学, 理学部, 教授 (40249751) ; TAMAKI Dai 信州大学, 理学部, 教授 (10252058) ; TSUKUDA Shuichi 琉球大学, 理学部, 准教授 (50305182)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 代数トポロジー / ホモトピー論 / ゲージ群 / ポリヘドラルプロダクト

Outline of Final Research Achievements

Homotopy noncommutativity of the loop product of loop spaces was studied through gauge groups and polyhedral products. As for gauge groups, the mod p decomposition, the classification of homotopy types of gauge groups corresponding to principal bundles with non-simply connected structure groups, and the classification of A_\infty types were achieved. Particularly, in the classification of A_\infty types, a new method to detect higher order Whitehead products by using Lanne T-functor was developed. As for polyhedral products, the fat wedge filtration was introduced, and through analyzing its structure, the homotopy types of polyhedral products were described. As is application. a topological proof of Golodness of certain simplicial complexes, which has been studied in combinatorial commutative algebra, was given.

Free Research Field

代数トポロジー