论文标题
模棱两可
Equivariant cohomology and depth
论文作者
论文摘要
令$ n \ geq 1 $为一个整数，让$ v =（\ mathbb {z}/2 \ mathbb {z}）^{n} $，让$ x $为$ v $ -cw-cw-complex。如果$ x $是有限的$ cw $ -complexe，则$ V $ -V $ -CW-COMPLEXE $ X $的同性恋模量，由$ h_ {v}^}^{*}（x，x，x，x，\ mthbb {f} _ {2}）$ $ 2 $ 2 $ 2 $ 2 $ 2 $ 2由$ h^{*}（v，\ mathbb {f} _ {2}）$表示。令$ dth_ {h^{*} v} h_ {v}^{*}（x，x，\ mathbb {f} _ {2}）$是有限类型$ h^{*}（v，v，v，\ m mathb {f} _ {2} _ {2} _ {2} _ {2}）$ - 模块$ - H_ _ _} \ Mathbb {f} _ {2}）$相对于增强理想，$ \ widetilde {h^{*}}}（v，\ mathbb {f} _ {2} _ {2}） \ Medskip \\本文的目的是证明以下结果：\ Medskip \\ {\ bf theorem}：对于每个子组$ w $ $ v $的$ w $ of $ v $，我们都有：$ dth_ {h^{*} w} w} h_ {w} h_ {w} dth_ {h^{*} v} h_ {v}^{*}（x，x，\ mathbb {f} _ {2}）$。
Let $n \geq 1$ be an integer, let $V=(\mathbb{Z}/2\mathbb{Z})^{n}$ and let $X$ be a $V$-CW-complex. If $X$ is a finite $CW$-complexe, the equivariant modulo $2$ cohomology of the $V$-CW-complexe $X$, denoted by $H_{V}^{*}(X, \mathbb{F}_{2})$, is a finite type module over the modulo $2$ cohomology of the group $V$, denoted by $H^{*}(V, \mathbb{F}_{2})$. Let $dth_{H^{*}V}H_{V}^{*}(X, \mathbb{F}_{2})$ be the depth of the finite type $H^{*}(V, \mathbb{F}_{2})$-module $H_{V}^{*}(X, \mathbb{F}_{2})$ relatively to the augmentation ideal, $\widetilde{H^{*}}(V, \mathbb{F}_{2})$, of $H^*(V, \mathbb{F}_{2})$. \medskip\\ The aim of this paper is to prove the following result: \medskip\\ {\bf Theorem}: For every subgroup $W$ of $V$, we have: $dth_{H^{*}W}H_{W}^{*}(X, \mathbb{F}_{2}) \leq dth_{H^{*}V} H_{V}^{*}(X, \mathbb{F}_{2}) $.
