Applications of real singularity theory and the homotopy types of spaces of holomorphic maps

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400083
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: The University of Electro-Communications
• Principal Investigator: YAMAGUCHI Kohhei 電気通信大学, 大学院情報理工学研究科, 教授 (00175655)
• Co-Investigator(Kenkyū-buntansha): Guest Martin 早稲田大学, 理工学術院, 教授 (10295470) ; 山田 裕一 電気通信大学, 大学院情報理工学研究科, 教授 (30303019) ; 島川 和久 岡山大学, 自然科学研究科, 特命教授 (70109081) ; 大野 真裕 電気通信大学, 大学院情報理工学研究科, 准教授 (70277820)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: ホモトピー型 / 正則写像 / 複素多様体 / 実代数的多様体 / トーリック多様体 / 終結式 / 手術 / 実特異点

Outline of Final Research Achievements

For complex manifolds X and Y (resp. real algebraic varieties X and Y), let Hol(X,Y) (resp. Alg(X,Y)) denote the space of holomorphic maps (resp. algebraic maps represented by polynomials) from X to Y. In this situation, we consider the inclusion map from Hol(X,Y) or Alg(X,Y) into the space Map(X,Y) of all continuous maps from X to Y, and we would like to investigate what dimension this inclusion map approximates the infinite dimensional space Map(X,Y). This problem is called the Atiyah-Jones-Segal conjecture. In particular, in this research we generalize the result of G. Segal concerning to the space of rational functions.

Free Research Field

幾何学（トポロジー）