References question - Compute $H_q(\mathbb R,\mathbb Q)$

Question

There exists a book that computes $H_q(\mathbb R,\mathbb Q)$ for all $q\in\mathbb N$?

I only find one for $q=0$

Many thanks!

Answer 1

If you use the long exact sequence of the pair $(\mathbb{R}, \mathbb{Q})$, you can calculate the higher homology groups since all the higher homology groups of $\mathbb{R}$ and $\mathbb{Q}$ are $0$.

In particular, $H_1(\mathbb{R},\mathbb{Q})\cong H_0(\mathbb{Q})\cong \bigoplus_\mathbb{Q}\mathbb{Z}$ and higher homology groups vanish.