Research on the stable homotopy category using quasi-categories

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400092
• 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: Torii Takeshi 岡山大学, 自然科学研究科, 准教授 (30341407)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 安定ホモトピー圏 / quasi-category / モデル圏 / Bousfield局所化 / 導来圏 / 表現のモジュライ / Morava K理論

Outline of Final Research Achievements

I have studied the stable homotopy category and its localizations by means of quasi-categories. Through spectral sequences, the stable homotopy category and its Bousfield localizations are considered to be related to the categories of representations for some groups and their derived categories. I gave a formulation of this relationship through the theories of model categories and quasi-categories. I have also constructed a functor between algebraic models of Bousfield localizations of the stable homotopy category via Morava K-theories. Furthermore, based on these, I have also studied more general moduli spaces of representations.

Free Research Field

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