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Prove that $S^n /{p,q}$ is homotopy equivalent to $S^n vee S^1$.

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2 1 $begingroup$ Prove that $S^n /{p, q}$ homotopy equivalent to $S^n ∨ S^1$ My attempt: I can see the picture quite clearly: But how to write explicit homotopies ? Thanks in Advance for help! algebraic-topology homotopy-theory share | cite | improve this question edited Nov 3 '18 at 15:10 Tyrone 4,505 1 12 25 asked Nov 3 '18 at 15:01 Coherent Coherent 1,230 5 23 $endgroup$