Betti numbers of 3-manifolds (Ex)

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Let $G$ be the fundamental group of a closed orientable $3$-manifold. Show that $b_2(G) \le b_1(G)$.
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Let $G$ be the fundamental group of a closed orientable $3$-manifold. Show that $b_2(G) \leq b_1(G)$.
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[[Category:Exercises]]
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[[Category:Exercises without solution]]

Revision as of 08:45, 6 January 2019

Let G be the fundamental group of a closed orientable 3-manifold. Show that b_2(G) \leq b_1(G). 
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