标题： 连通功率运算和单纯庞加莱对偶性 显示英文标题

标题： Connected power operations and simplicial Poincaré duality

摘要： 我们引入了一种称为“连通循环对角”的链复形结构，它在其上同调中诱导出稳定的幂运算，并且具有负幂运算始终消失的性质。 这种链层次结构有助于表示谱的幂运算，其上同调缺乏乘积。 利用标准增单形的整数链上的庞加莱对偶代数结构，我们提供了一种有效的方法来构造广泛类别的增单形对象上的循环对角。 显示英文摘要

摘要： We introduce a structure termed ``connected cyclic diagonal'' on a chain complex, which induces stable power operations in its cohomology with the property that negative power operations consistently vanish. This chain level structure is useful to represent power operations for spectra, whose cohomology lacks a cup product. Using a Poincar\'e duality algebra structure on the integral chains of the standard augmented simplex, we provide an effective method for the construction of cyclic diagonals on a broad class of augmented simplicial objects.