[Un invariant des trois-variétés qui compte des configurations de graphes]
The logarithm of the Kontsevich–Kuperberg–Thurston invariant counts embeddings of connected trivalent graphs in an oriented rational homology sphere, using integrals on configuration spaces of points in the given manifold. It is a universal finite type invariant of oriented rational homology spheres. The exponential of this invariant is often called the perturbative expansion of the Chern–Simons theory. In this article, we give an independent original definition of the degree two part of the logarithm of the Kontsevich–Kuperberg–Thurston invariant appropriate for concrete computations. This article can also serve as an introduction to the general definition of the Kontsevich–Kuperberg–Thurston invariant.
Le logarithme de l’invariant de Kontsevich–Kuperberg–Thurston d’une sphère d’homologie rationnelle compte des plongements de graphes trivalents et connexes dans cette variété. Il est défini à partir d’intégrales sur des espaces de configurations de points dans la variété en question. Il s’agit d’un invariant universel de type fini des sphères d’homologie rationnelle. Son exponentielle est souvent appelée expansion perturbative de la théorie de Chern–Simons. Dans cet article, nous donnons une définition indépendante et originale de la partie de degré deux du logarithme de l’invariant de Kontsevich–Kuperberg–Thurston. Cette définition est d’usage plus commode pour des calculs concrets. Cet article peut également servir d’introduction à la définition générale de l’invariant de Kontsevich–Kuperberg–Thurston.
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Keywords: low-dimensional topology, invariants of three-dimensional manifolds, configuration spaces, finite type invariants, Chern–Simons theory
Yohan Mandin--Hublé 1
CC-BY 4.0
@article{AFST_2025_6_34_5_1433_0,
author = {Yohan Mandin--Hubl\'e},
title = {A three-manifold invariant from graph configurations},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {1433--1473},
year = {2025},
publisher = {Universit\'e de Toulouse, Toulouse},
volume = {Ser. 6, 34},
number = {5},
doi = {10.5802/afst.1837},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1837/}
}
TY - JOUR AU - Yohan Mandin--Hublé TI - A three-manifold invariant from graph configurations JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2025 SP - 1433 EP - 1473 VL - 34 IS - 5 PB - Université de Toulouse, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1837/ DO - 10.5802/afst.1837 LA - en ID - AFST_2025_6_34_5_1433_0 ER -
%0 Journal Article %A Yohan Mandin--Hublé %T A three-manifold invariant from graph configurations %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2025 %P 1433-1473 %V 34 %N 5 %I Université de Toulouse, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1837/ %R 10.5802/afst.1837 %G en %F AFST_2025_6_34_5_1433_0
Yohan Mandin--Hublé. A three-manifold invariant from graph configurations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 34 (2025) no. 5, pp. 1433-1473. doi: 10.5802/afst.1837
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