论文标题
rep rep的弗雷恩斯定理（$ c_2 $） - 复合体
The freeness theorem for equivariant cohomology of Rep($C_2$)-complexes
论文作者
论文摘要
令$ c_2 $为第二订单的循环组。我们表明，有限代表（$ C_2 $）的$ RO（C_2）$ - 分级的Bredon共同体 - 复杂作为模块免费，而不是Constant Mackey Foundator $ \ usepline {\ mathbb {f} _2} $的模块。本文纠正了克朗霍尔姆（Kronholm）的这种烦恼定理的一些错误。它还将FREENESS结果扩展到有限型复合体，每个复合物具有每个固定设定尺寸的许多单元格。我们给出一个反例，显示定理对局部有限的复合物不满意。
Let $C_2$ be the cyclic group of order two. We show that the $RO(C_2)$-graded Bredon cohomology of a finite Rep($C_2$)-complex is free as a module over the cohomology of a point when using coefficients in the constant Mackey functor $\underline{\mathbb{F}_2}$. This paper corrects some errors in Kronholm's proof of this freeness theorem. It also extends the freeness result to finite type complexes, those with finitely many cells of each fixed-set dimension. We give a counterexample showing the theorem does not hold for locally finite complexes.
