Research on homotopy theory and reconstruction of spaces using categories
| Project/Area Number |
15K17535
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Shinshu University |
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Principal Investigator |
TANAKA Kohei 信州大学, 学術研究院社会科学系, 助教 (70708362)
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| Research Collaborator |
TAMAKI Dai 信州大学, 学術研究院理学系, 教授 (10252058)
NANDA Vidit The University of Oxford
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| Project Period (FY) |
2015-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 圏 / ホモトピー論 / センサーネットワーク / オイラー積分 / LS カテゴリー / 離散モース理論 / ＬＳカテゴリー / オイラー標数 / LS-category |
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| Outline of Final Research Achievements |
In this research, we established the combinatorial homotopy theory and its application based on categories, which consists of points and arrows. Given an acyclic flow on a cell complex, we obtained a category from the critical cells and reconstructed the information of the original space. On the other hand, we introduced a discrete invariant of partially ordered sets as a tool to classify them.
As an application of these theory, we considered the counting problem for targets lying on a sensor network. By using the integration with respect to combinatorial Euler characteristic, we showed that we can compute the number of targets lying on the network graph.
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Report
(3 results)
Research Products
(9 results)
