2017 Fiscal Year Final Research Report
Moduli spaces of linear representations and non-abelian torsion invariants
| Project/Area Number |
26800032
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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 | The University of Tokyo (2016-2017)
Tokyo Institute of Technology (2014-2015) |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 3次元多様体 / 位相不変量 / 表現 |
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| Outline of Final Research Achievements |
The project aimed at mutual development of the studies on spaces of linear representations of fundamental groups and non-abelian torsion invariants of 3-manifolds. As a result we showed that all surfaces essentially splitting 3-manifolds are constructed from points at infinity of spaces of representations of high dimensions. Regarding torsion invariants as functions on spaces of linear representations, we also discovered that the homology classes of surfaces constructed from points at infinity are restricted by certain regularity at the points of the functions. Moreover, from the point of view of arithmetic topology we introduced a new type of torsion invariants for knots defined from deformations of representations of dimension 2 over finite fields.
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| Free Research Field |
位相幾何学
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