2013 Fiscal Year Final Research Report
Topology related to graph complex
| Project/Area Number |
23740040
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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 | Shimane University (2013)
Hokkaido University (2011-2012) |
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Principal Investigator |
WATANABE Tadayuki 島根大学, 総合理工学研究科(研究院), 講師 (70467447)
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| Project Period (FY) |
2011 – 2013
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| Keywords | Morse-Novikov理論 / Morse理論 / Chern-Simons摂動理論 / グラフ複体 / 3次元多様体 / 微分同相群 / 曲面束 |
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| Research Abstract |
We introduced the notion of ``amidakuji-like path'' in a closed 3-manifold M that is a surface bundle over the circle and applied it to the construction of a Z-equivariant invariant of M. An amidakuji-like path is a piecewise smooth path in M and can be considered as an approximation of an integral curve for the gradient vector field of the projection of the surface bundle. As an analogue of Kenji Fukaya's Morse homotopy theory, we obtained a candidate for a Z-equivariant invariant by counting 3-valent graphs in M whose edges are amidakuji-like paths.
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