Huang's relative Artin complex conjecture
Huang's relative Artin complex conjecture
Let be an Artin group with defining graph , and let denote the relative Artin complex spanned by vertices of types indexed by . Suppose is a complete graph with vertex set , and is such that is almost spherical. If and the subgraph spanned by are both connected and free of infinity, Huang's conjecture.
Here being almost spherical means that its defining graph is free of infinity, is not finite type, and every proper standard subgroup with is finite type. The conjecture is stated as equivalent to the conjecture in the cited work. Elias and Williamson initially claimed that it had been proved, but retracted that claim, so it remains open.
Sources & referencesView supporting material
Primary source
Rachael Boyd, “An introduction to the geometric and combinatorial group theory of Artin groups”, arXiv:2601.08658 (2026).
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