Analyticity of the Free Energy of a Closed 3-Manifold

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dc.creatorGaroufalidis, Stavros
dc.creatorLe, Thang T. Q.
dc.creatorMarino, Marcos
dc.date2008-09-15
dc.date2008-11-15
dc.date.accessioned2026-07-07T10:18:19Z
dc.date.available2026-07-07T10:18:19Z
dc.descriptionThe 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.
dc.descriptionThis is a contribution to the Special Issue on Deformation Quantization, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/0809.2572
dc.identifierhttp://arxiv.org/abs/0809.2572
dc.identifierSIGMA 4 (2008), 080, 20 pages
dc.identifierdoi:10.3842/SIGMA.2008.080
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174147
dc.subjectGeometric Topology
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.subject57M27
dc.titleAnalyticity of the Free Energy of a Closed 3-Manifold
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