It is said that $\mathbb R P^n \to \mathbb R P^n/\mathbb R P^{n-1}$ induces isomorphism on $H_n$ when $n$ is odd. How can we prove this?
How can we prove that $\mathbb R P^n \to \mathbb R P^n/\mathbb R P^{n-1}$ induces isomorphism on $H_n$ when n is odd?
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algebraic-topology
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1Compute the cellular homology groups of both, check they're isomorphic. Look at the proof that cellular homology computes singular homology and see that it implies e$x$actly what you want. – 2012-04-04