Strongly obstructed combinatorics limit conjecture

Consider strongly obstructed combinatorics in the bimodal regions of topological shapes +++-+ and +-+-, and let (Σ,Δ)(\Sigma,\Delta) denote the moduli coordinates. In the unimodal case, let a minimal combinatorics mean one of the minimal combinatorial types considered in the source. Strongly obstructed combinatorics limit conjecture. For strongly obstructed combinatorics, the only possible limit is (.5,1)(-.5,1) in the +++-+ case, or (+.5,1)(+.5,1) in the +-+- case. Every minimal combinatorics in the unimodal case is unobstructed. This is presented as a consequence of the preceding conjectural alternative and supplements the claim that minimal unimodal combinatorics are unobstructed; the source gives no resolution.

Sources & referencesView supporting material

Primary source

Araceli Bonifant, John Milnor and Scott Sutherland, “The W. Thurston Algorithm for Real Quadratic Rational Maps”, arXiv:2009.10147 (2020).

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