How to compute the homology group of $SO(n)$?
I can calculate the homology group of $SO(n)$ when $n\leq3$.eg,$SO(3)\cong RP^3$,but I have no idea when $n>4$.I tried to use the exact sequence of relative homology group.What is the homology of $H_n(SO(n)\setminus\{I_n\})$?