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arXiv · 2607.07886

Combining cusped triangle groups with Blaschke products: commensurable matings

Yusheng Luo·Mahan Mj·Sabyasachi Mukherjee
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Abstract

In this note, we construct algebraic correspondences as matings of Fuchsian $(p,q,\infty)$-triangle groups with Blaschke products. Combined with the results of [MM25], this proves mateability of all cusped triangle groups with suitable Blaschke products. The proof of the main result involves associating two piecewise analytic circle maps to the $(p,q,\infty)-$triangle group, mating these maps with appropriate Blaschke products to produce two commensurable conformal matings, and finally constructing the desired algebraic correspondence as a common lift of the two conformal matings.

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Yusheng Luo, Mahan Mj, Sabyasachi Mukherjee. 2026-07-08. Combining cusped triangle groups with Blaschke products: commensurable matings. https://arxiv.org/abs/2607.07886

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