辛$\mathbb{Z}_2^n$ -流形
Symplectic $\mathbb{Z}_2^n$-manifolds
摘要：
粗略地说，$\mathbb{Z}_2^n$ -流形是配备有$\mathbb{Z}_2^n$ -分次交换坐标的“流形”，符号规则由它们的$\mathbb{Z}_2^n$ -度的标量积确定。我们研究了辛$\mathbb{Z}_2^n$ -流形的概念，即，一个$\mathbb{Z}_2^n$ -流形，它配备了一个辛二形式，可以携带非零的$\mathbb{Z}_2^n$ -度。我们表明，辛几何的基本概念和结果推广到“高年级”的设置，包括达布定理的推广。
英文摘要：
Roughly speaking, $\mathbb{Z}_2^n$-manifolds are `manifolds' equipped with $\mathbb{Z}_2^n$-graded commutative coordinates with the sign rule being determined by the scalar product of their $\mathbb{Z}_2^n$-degrees. We examine the notion of a symplectic $\mathbb{Z}_2^n$-manifold, i.e., a $\mathbb{Z}_2^n$-manifold equipped with a symplectic two-form that may carry non-zero $\mathbb{Z}_2^n$-degree. We show that the basic notions and results of symplectic geometry generalise to the `higher graded' setting, including a generalisation of Darboux's theorem.
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。
