A study on homotopy sets and families of homotopy invariant subsets

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K04884
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Fukuoka University
• Principal Investigator: ODA Nobuyuki 福岡大学, 理学部, 教授 (80112283)
• Project Period (FY): 2015-10-21 – 2019-03-31
• Keywords: 幾何学 / トポロジー

Outline of Final Research Achievements

A theorem is proved on the relation between cofibrations and the self-closeness numbers, and its dual, that is, a theorem on the relation between fibrations and the self-closeness numbers. The K group of the ring of continuous functions for spaces with special conditions is presented by cohomology groups. A result is proved on the homotopy set of maps which preserve cyclic elements and its dual. A theorem is proved about the groups of the self homotopy equivalences of smash products of a space and the semi-direct products of the direct product of the groups of the self homotopy equivalences of the space and the symmetric groups, and moreover, some general results are proved making use of cohomology groups.

Free Research Field

数学

Academic Significance and Societal Importance of the Research Achievements

自己親密数に関する結果は新しい結果であり，特に，コファイブレイションおよびファイブレイションと自己親密数に関する定理は今後の研究に有用である．連続関数環のK群に関する結果，サイクリック元を保存する写像のホモトピー集合とその双対の結果，コゴトリーブ集合について特別な場合に短完全列が存在すること，空間の約積の自己ホモトピー同値写像類の群と空間の自己ホモトピー同値写像類の群と対称群の半直積との関係を与える定理は新しい研究の基礎となる結果であり，これらの分野の今後の研究に役立つ．