2023 Fiscal Year Final Research Report
Study on dimension and topological spaces in coarse geometry
Project/Area Number |
19K03467
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 11020:Geometry-related
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Research Institution | Ehime University |
Principal Investigator |
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Project Period (FY) |
2019-04-01 – 2024-03-31
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Keywords | 粗幾何学 / 次元 / 位相空間 |
Outline of Final Research Achievements |
We studied notions related to dimension in coarse geometry and topological spaces which reflect coarse geometric properties of metric spaces. As for dimension, we obtained results on coarse embeddability of hyperspaces consisting of finite subsets into a Hilbert space, and on transfinite asymptotic dimension, which is a transfinite extension of asymptotic dimension. As for topological spaces, we obtained results on coarse compactifications by means of generalized Gromov products, and on connectedness properties of the Higson corona of the half line. We also studied group coarse structures and dimensions defined for group actions.
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Free Research Field |
幾何学
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Academic Significance and Societal Importance of the Research Achievements |
有限集合からなる超空間のHilbert空間への粗埋め込み可能性の研究は、Gromov-Hausdroff距離空間の研究へ発展している。超限漸近次元に関する成果によって、Dydakによって導入された漸近的性質Dを超限漸近次元を用いて特徴付けることができた。一般化されたGromov積による粗コンパクト化の成果によって、粗コンパクト化の新たな記述が可能となった。半直線のHigsonコロナの連結性に関する成果によって、Higsonコロナの複雑な位相的性質を顕在化できた。
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