有限Q坏空间
A finite Q-bad space
摘要：
证明了对于自由非循环群$F$，$H_2(\hat F_\mathbb Q, \mathbb Q)$是不可数的$\mathbb Q$ -向量空间.这里$\hat F_\mathbb Q$是$F$的$\mathbb Q$ -完成。这回答了A.K. Bousfield对于有理系数的情形。作为这个结果的直接结果，可以得出这样的结论：在Bousfield-Kan意义上，一个楔形圆是$\mathbb Q$ -坏的。用与证明上述结果相同的方法，证明了同调$H_2(\hat F_\mathbb Z,\mathbb Z)$是不可可除群，其中$\hat F_\mathbb Z$是$F$的整数幂等完备化.
英文摘要：
We prove that for a free noncyclic group $F$, $H_2(\hat F_\mathbb Q, \mathbb Q)$ is an uncountable $\mathbb Q$-vector space. Here $\hat F_\mathbb Q$ is the $\mathbb Q$-completion of $F$. This answers a problem of A.K. Bousfield for the case of rational coefficients. As a direct consequence of this result it follows that, a wedge of circles is $\mathbb Q$-bad in the sense of Bousfield-Kan. The same methods as used in the proof of the above results allow to show that, the homology $H_2(\hat F_\mathbb Z,\mathbb Z)$ is not divisible group, where $\hat F_\mathbb Z$ is the integral pronilpotent completion of $F$.
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。
