锚定泡沫和环空同源性

IF 0.6 3区数学 Q3 MATHEMATICS Algebraic and Geometric Topology Pub Date : 2023-09-26 DOI:10.2140/agt.2023.23.3129

Rostislav Akhmechet, Mikhail Khovanov

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引用次数: 5

摘要

通过泡沫评价，我们描述了固体环面中链接的等变SL(2)和SL(3)同源性。实体环面被三维空间替换，其中有一条不同的线。环形腹板状态空间的生成器用泡沫表示，泡沫的边界可能与区分线相交;交点，称为锚点，为泡沫评估提供了额外的术语，让人想起黑森的平方根。本文对定向和无取向SL(3)泡沫进行了处理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Anchored foams and annular homology

We describe equivariant SL(2) and SL(3) homology for links in the solid torus via foam evaluation. The solid torus is replaced by 3-space with a distinguished line in it. Generators of state spaces for annular webs are represented by foams with boundary that may intersect the distinguished line; intersection points, called anchor points, contribute additional terms, reminiscent of square roots of the Hessian, to the foam evaluation. Both oriented and unoriented SL(3) foams are treated in the paper.

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