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arXiv · 2604.11327

Wheel Classes in Kontsevich Graph Complex and Merkulov's Low-Valence Conjecture

Assar Andersson
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Abstract

We show that the wheel classes in the Kontsevich graph complex $GC_d$ admit representatives supported on graphs with only $3$- and $4$-valent vertices. This verifies that Merkulov's low-valence conjecture holds for the wheel classes. More precisely, for every $m \ge 2$, we prove that the wheel graph $W_{2m+1}$ is homologous to an explicit linear combination of $2^{m-2}$ graphs, each having only $3$- and $4$-valent vertices.

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Assar Andersson. 2026-04-13. Wheel Classes in Kontsevich Graph Complex and Merkulov's Low-Valence Conjecture. https://arxiv.org/abs/2604.11327

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