Wheel Classes in Kontsevich Graph Complex and Merkulov's Low-Valence Conjecture
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910238378033152 |
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| author | Andersson, Assar |
| author_facet | Andersson, Assar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11327 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wheel Classes in Kontsevich Graph Complex and Merkulov's Low-Valence Conjecture Andersson, Assar Quantum Algebra Combinatorics 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. |
| title | Wheel Classes in Kontsevich Graph Complex and Merkulov's Low-Valence Conjecture |
| topic | Quantum Algebra Combinatorics |
| url | https://arxiv.org/abs/2604.11327 |