Betti numbers of 3-manifolds (Ex)

Let $G$$<wikitex>; Let $G$ be the fundamental group of a closed orientable $-manifold. Show that $b_2(G) \leq b_1(G)$. </wikitex> [[Category:Exercises]] [[Category:Exercises with solution]]G$ be the fundamental group of a closed orientable $3$$3$-manifold. Show that $b_2(G) \leq b_1(G)$$b_2(G) \leq b_1(G)$.