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On the Cohomology of Two Stranded Braid Varieties

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arxiv 2312.03283 v2 pith:2UR4P7RJ submitted 2023-12-06 math.AG math.RT

Tonie Scroggin This is my paper · ORCID
classification math.AGmath.RT
keywords braidvarietiescohomologiesalexanderclustercohomologycomputeconfirm
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We compute the cohomologies of two strand braid varieties using the two-form present in cluster structures. We confirm these results with proof using Alexander and Poincar\'e duality. Further, we consider products of braid varieties and their interactions with the cohomologies.

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  1. Splicing braid varieties

    math.AG 2025-05 conditional novelty 6.0 of 10

    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.

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