A three-manifold invariant from graph configurations

Yohan Mandin-Hublé

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arXiv · 2311.16972

A three-manifold invariant from graph configurations

Yohan Mandin-Hublé

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Abstract

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 logarithm of the Kontsevich-Kuperberg-Thurston invariant.

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Yohan Mandin-Hublé. 2023-11-28. A three-manifold invariant from graph configurations. https://arxiv.org/abs/2311.16972

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