Research on the topology of configuration spaces by means of combinatorial methods and its applications
Project/Area Number |
23540082
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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 |
Research Field |
Geometry
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Research Institution | Shinshu University |
Principal Investigator |
TAMAKI Dai 信州大学, 学術研究院理学系, 教授 (10252058)
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Project Period (FY) |
2011-04-28 – 2015-03-31
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Project Status |
Completed (Fiscal Year 2014)
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Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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Keywords | stratified space / configuration space / small category / classifying space / topological category / 分類空間 / 位相圏 |
Outline of Final Research Achievements |
A cell complex is a topological space which is a union of balls of various dimensions in a nice way. Such a structure has benn proved to be very useful in topology and related fields. In this research, a new notion of cellular stratified spaces is introduced as a generalization of cell complexes. One of the main results is that, for a cellular stratified space satisfying a certain condition, we obtain a topological category, called the face category, whose classifying space can be embedded in the original space as a deformation retract. It means that the classifying space is homotopy equivalent to the original space. This result can be used, for example, to determine the fundamental group of the configuration space of a graph of small size.
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Report
(5 results)
Research Products
(22 results)
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[Presentation] トポロジカル相からK理論へ2014
Author(s)
玉木 大
Organizer
Summer School数理物理
Place of Presentation
東京大学大学院数理科学研究科
Year and Date
2014-08-29 – 2014-08-31
Related Report
Invited
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