发表机构
University of Warsaw; Harvard University（华沙大学; 哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文发展了Laurent环上配对缺陷的庞加莱对偶理论，通过球面三角剖分构造平坦分解，并利用等变上同调建立二次细化，进而证明高维泡利稳定子码辫子配对的非退化性。
AI 中文摘要
我们发展了Laurent多项式环上非退化双线性配对缺陷的庞加莱对偶理论。一个关键要素是特征模的一种新的平坦分解，该分解由与扇相关联的无穷远球面的三角剖分构造而成。此分解上的杯积将球面上的庞加莱对偶转化为所得缺陷模之间的典范配对。在中间度数上，我们利用具有对径作用的球面的等变上同调构造了显著的二次细化。用射影空间有效替换球面为除以二提供了几何替代。应用于平移不变的泡利稳定子码时，我们的结果确立了高维辫子配对的非退化性。它们将二维拓扑自旋的T型结公式推广到更高维度，并赋予其几何解释。
英文摘要
We develop a Poincaré duality theory for defects of nondegenerate sesquilinear pairings over Laurent polynomial rings. A key ingredient is a novel flat resolution of the character module, constructed from a triangulation of the sphere at infinity associated with a fan. The cup product on this resolution turns Poincaré duality on the sphere into canonical pairings between the resulting defect modules. In middle degrees, we construct distinguished quadratic refinements using equivariant cohomology of the sphere with the antipodal action. The effective replacement of the sphere with a projective space provides a geometric substitute for division by two. Applied to translation-invariant Pauli stabilizer codes, our results establish the nondegeneracy of higher-dimensional braiding pairings. They extend the two-dimensional T-junction formula for topological spin to higher dimensions, while giving it a geometric interpretation.
