论文标题
gysin_v命令
Gysin_V-functors
论文作者
论文摘要
令$ d \ geq 1 $为整数，$ \ mathcal {k} _ {d} $是$（\ Mathbb {z}/2 \ Mathbb {z}} $ grounite and grienite and griped and of Gragenite and griped and of Grade and Primite of Gradeed and Litecor的$（\ Mathbb {Z}/2 \ Mathbb {Z}/2 $ \ mathbb {f} _ {2} $ - 代数。在本文中，我们将G. Carlsson的猜想推广到$（\ Mathbb {Z}/2 \ Mathbb {Z}）^{d} $的免费动作上gysin- $（\ mathbb {z}/2 \ mathbb {z}）^{d} $ - functor（也就是说，可以说，函数$ \ mathcal {k} _ {d} $满足某些属性），那么我们有：$ \ big（c_ {d}}} {d} \ big big; \ unterSet {i \ geq 0} {\ sum} dim _ {\ mathbb {f} _ {2}} \ big（\ mathcal {k} _ {d} _ {d} _ {d}（0）\ big）我们表明，在某些情况下，我们获得了以下结果的独立证明。\\定理。如果组$（\ Mathbb {z}/2 \ Mathbb {z}）^{d} $，$ 1 \ leq d \ leq 3 $，在有限的CW-Complex $ x $上自由地和手机，然后$ x $，然后$ { 0} {\ sum}} dim _ {\ mathbb {f} _ {2}} h^{i}（x; \; \; \; \; \; \; \;
Let $d \geq 1$ be an integer and $\mathcal{K}_{d}$ be a contravariant functor from the category of subgroups of $(\mathbb{Z}/2\mathbb{Z})^{d}$ to the category of graded and finite $\mathbb{F}_{2}$-algebras. In this paper, we generalize the conjecture of G. Carlsson, concerning free actions of $(\mathbb{Z}/2\mathbb{Z})^{d}$ on finite CW-complexes, by suggesting, that if $\mathcal{K}_{d}$ is a Gysin-$(\mathbb{Z}/2\mathbb{Z})^{d}$-functor (that is to say, the functor $\mathcal{K}_{d}$ satisfies some properties), then we have: $\big(C_{d} \big): \; \underset{i \geq 0}{\sum}dim_{\mathbb{F}_{2}} \big(\mathcal{K}_{d}(0)\big)^{i} \geq 2^{d}$.\\ We prove this conjecture for $1 \leq d \leq 3$ and we show that, in certain cases, we get an independent proof of the following result.\\ Theorem. If the group $(\mathbb{Z}/2\mathbb{Z})^{d}$, $ 1 \leq d \leq 3$, acts freely and cellularly on a finite CW-complex $X$, then ${\underset{i \geq 0}{\sum}}dim_{\mathbb{F}_{2}}H^{i}(X;\; \mathbb{F}_{2}) \geq 2^{d}$.
