容许扭结空间的切除定理
Excision for Spaces of Admissible Skeins
AI总结：
本文定义了S-容许扭结模，证明任意维度下该模满足切除定理，还关联了不同子范畴下的扭结模，将结果应用于柱范畴并重建其与修正迹的关系。
摘要：
d维流形的扭结模是由嵌入的带标架图张成的向量空间，这些图由范畴A装饰，且带有依赖于维度d的合适额外结构，并模去d维球内部成立的局部关系。对于A的一个满子范畴S，S-容许扭结模以类似方式定义，区别在于给定球的局部关系仅当球外至少有一条边被S着色时才可应用。\n本文证明了任意维度下的容许扭结模都满足切除性质，即粘合流形的扭结模可表示为被粘合边界分量上边界值的余端。我们还建立了不同S选择下扭结模之间的联系，将结果应用于柱范畴，并重新得到了其与修正迹的关系。
英文摘要：
The skein module for a d-dimensional manifold is a vector space spanned by embedded framed graphs decorated by a category A with suitable extra structure depending on the dimension d, modulo local relations which hold inside d-balls. For a full subcategory S of A, an S-admissible skein module is defined analogously, except that local relations for a given ball may only be applied if outside the ball at least one edge is coloured in S. In this paper we prove that admissible skein modules in any dimension satisfy excision, namely that the skein module of a glued manifold is expressed as a coend over boundary values on the boundary components glued together. We furthermore relate skein modules for different choices of S, apply our result to cylinder categories, and recover the relation to modified traces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
