On perturbative invariants of combed three-manifolds

Yohan Mandin--Hublé

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arXiv · 2510.19633

On perturbative invariants of combed three-manifolds

Yohan Mandin--Hublé

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Abstract

We give a new definition of a universal finite type invariant of three-dimensional oriented rational homology spheres which counts configurations of trivalent graphs in such manifolds. Kontsevich introduced this invariant following Witten's study of the perturbative expansion of the Chern-Simons theory, using parallelizations of three-manifolds. In this article, we use combings instead of parallelizations to get a more flexible and convenient definition.

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Yohan Mandin--Hublé. 2025-10-22. On perturbative invariants of combed three-manifolds. https://arxiv.org/abs/2510.19633

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