Developments of the geometric topology of homology manifolds with curvature bounded above
| Project/Area Number |
26610012
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | University of Tsukuba |
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Principal Investigator |
NAGANO Koichi 筑波大学, 数理物質系, 講師 (30333777)
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| Research Collaborator |
LYTCHAK Alexander ケルン大学
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| 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)
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| 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 |
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| 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).
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Report
(5 results)
Research Products
(2 results)
