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Developments of the geometric topology of homology manifolds with curvature bounded above

Research Project

Project/Area Number 26610012
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionUniversity of Tsukuba

Principal Investigator

NAGANO Koichi  筑波大学, 数理物質系, 講師 (30333777)

Research Collaborator LYTCHAK Alexander  ケルン大学
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords幾何学 / リーマン幾何(含幾何解析) / CAT(k)空間 / アレキサンドルフ空間 / ホモロジー多様体 / リーマン幾何(含幾何解析) / アレクサンドルフ空間
Outline of Final Research Achievements

For spaces with curvature bounded above, especially CAT(k) spaces, from viewpoints of Riemannian geometry and geometric topology, I have expanded the geometric topology of homology manifolds with curvature bounded above by studying the geometric structure metrically. I have mainly attempt to study the Riemannian differentiable structure on CAT(k) spaces, the Riemannian volume measure on CAT(k) spaces, the precompactness of CAT(k) spaces with respect to the measured Gromov-Hausdorff topology, and I have obtained several versatile research results as joint works with Alexander Lytchak (University of Cologne).

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (2 results)

All 2018 Other

All Int'l Joint Research (1 results) Journal Article (1 results) (of which Int'l Joint Research: 1 results,  Open Access: 1 results)

  • [Int'l Joint Research] ケルン大学(ドイツ)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Geodesically complete spaces with an upper curvature bound2018

    • Author(s)
      Alexander Lytchak and Koichi Nagano
    • Journal Title

      arXiv.org, preprint, arXiv:1804.05189.

      Volume: - Pages: 1-40

    • Related Report
      2017 Annual Research Report
    • Open Access / Int'l Joint Research

URL: 

Published: 2014-04-04   Modified: 2022-08-05  

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