2012 Fiscal Year Final Research Report
Study of perturbative quantum invariant of rational homology 3-spheres
| Project/Area Number |
22540073
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kyushu University |
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Principal Investigator |
TAKATA Toshie 九州大学, 数理学研究院, 准教授 (40253398)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 低次元トポロジー / 量子不変量 |
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| Research Abstract |
For a rational homology 3-sphre, the SU(N) free energy is a power series in 2 variables and an topological invariant of M. The SU(N) free energy can be obtained by applying the SU(N) weight system to the LMO invariant of M. By using a combinatorial way to compute the SU(N) weight system, we obtained an formula for any genus of the SU(N) free energy for Seifert homology 3-spheres. It can be written in terms of the generalized Catalan numbers. Especially, the genus 0 part of the free energy can be written in terms of the generalized Catalan numbers for genus 0 where parameters are even numbers. We gave a formula of these generalized Catalan numbers.
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