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What are sufficient conditions such that $\pi_1(X\vee Y)=\pi_1(X)\ast\pi_1(Y)$ for spaces $X$ and $Y$?

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    see the answer of http://math.stackexchange.com/questions/320812/fundamental-group-of-the-wedge-sum-of-two-spaces – user68316 Aug 10 '13 at 12:02

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For example if the pasting point has a contractible neighborhood in both spaces.

Edoardo Lanari
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  • how about a proof? –  Dec 07 '13 at 18:12
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    It's almost trivial if you know Van Kampen's theorem: just define $U_1:=X \cup V_1$ and $U_2:=Y \cup V_2$ where $V_1,V_2$ are the contractible neighborhood of the pasting point respectively in $Y$ and in $X$. – Edoardo Lanari Dec 07 '13 at 21:43