Work

$\mathfrak{sl}(2)$-weight system does not extend to a graph 4-invariant

Year: 2026

Type: preprint

Abstract: A long-standing question by S. Lando asks whether the $\mathfrak{sl}(2)$-weight system extends to a unique 4-invariant of graphs. We show that, in full generality, the answer to this question is negative. However, for certain specializations of the weight system, extensions do exist. Explicit formulae for computing two such specializations of the weight system are already known. We construct recurrence relations for one additional such extension and discuss the last remaining specialization, which conjecturally admits an extension. We also study the polynomial coefficients of the $\mathfrak{sl}(2)$-weight system and resolve the questions concerning their extension.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.24217

Authors: Fomichev, Daniil, Karev, Maksim, Pavutnitskiy, Fedor, Usanov, Sergey

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7171558046

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