Open sets in braid varieties defined by transversality to a coordinate flag are isomorphic to products of two simpler braid varieties, and in the double Bott-Samelson case this splicing respects cluster structures.
Cluster algebras
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Splicing braid varieties
Open sets in braid varieties defined by transversality to a coordinate flag are isomorphic to products of two simpler braid varieties, and in the double Bott-Samelson case this splicing respects cluster structures.