Analyticity of the Free Energy of a Closed 3-Manifold
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Analyticity of the Free Energy of a Closed 3-Manifold
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| Creator |
Garoufalidis, S.
Thang T.Q. Lê Mariño, M. |
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| Description |
The free energy of a closed 3-manifold is a 2-parameter formal power series which encodes the perturbative Chern-Simons invariant (also known as the LMO invariant) of a closed 3-manifold with gauge group U(N) for arbitrary N. We prove that the free energy of an arbitrary closed 3-manifold is uniformly Gevrey-1. As a corollary, it follows that the genus g part of the free energy is convergent in a neighborhood of zero, independent of the genus. Our results follow from an estimate of the LMO invariant, in a particular gauge, and from recent results of Bender-Gao-Richmond on the asymptotics of the number of rooted maps for arbitrary genus. We illustrate our results with an explicit formula for the free energy of a Lens space. In addition, using the Painlevé differential equation, we obtain an asymptotic expansion for the number of cubic graphs to all orders, stengthening the results of Bender-Gao-Richmond.
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| Date |
2019-02-19T12:21:34Z
2019-02-19T12:21:34Z 2008 |
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| Type |
Article
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| Identifier |
Analyticity of the Free Energy of a Closed 3-Manifold / S. Garoufalidis, Thang T.Q. Lê, M. Mariño // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 55 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 57N10; 57M25 http://dspace.nbuv.gov.ua/handle/123456789/148975 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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