Development of homotopy theoretic methods in the study of diffeological spaces

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540081
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Okayama University
• Principal Investigator: SHIMAKAWA Kazuhisa 岡山大学, 自然科学研究科, 教授 (70109081)
• Co-Investigator(Kenkyū-buntansha): YAMAGUCHI Kohhei 電気通信大学, 情報理工学(系)研究科, 教授 (00175655)
• Co-Investigator(Renkei-kenkyūsha): HARAGUCHI Tadayuki 大分工業高等専門学校, 一般科理系, 講師 (60633708)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 微分空間 / モデル圏 / Quillen 同値 / de Rham コホモロジー

Outline of Final Research Achievements

In order to establish the foundation of homotopy theory of diffeological spaces, we constructed on the category of diffeological spaces a finitely generated model structure having smooth weak homotopy equivalences as the class of of weak equivalences. It has been shown that our model structure on the category of diffeological spaces is Quillen equivalent to the standard Quillen model structure on the category of topological spaces, with weak homotopy equivalences as the class of weak equivalences.

Free Research Field

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