A finite Q-bad space

Sergei O. Ivanov, Roman Mikhailov

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 o…