# Is the wedge sum of two cones over the hawaiian earring contractible?

Let $X_1$ and $X_2$ be two cones over the hawaiian earring and let $X$ be the wedge sum of $X_1$ and $X_2$ (of course you join them in the special point of the hawaiian earring). How do you prove that $X$ is not contractible? Thanks

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@Pedro: If this is a homework, then MO is not an appropriate place for the question, try math.stackexchange instead. If this is not a homework, you should give a motivation for the question, explain why do you think the space is not contractible, what did you try to solve this problem, etc. –  Misha Dec 21 '12 at 18:06
Also: Try to search "wedge sum" on MO; the first hit you see will get you started on the problem regardless of its origin. –  Misha Dec 21 '12 at 18:18

See the proof of Theorem 2.6 of

J.W. Cannon, G.R. Conner, The combinatorial structure of the Hawaiian Earring group, Topology Appl. 106 (3) (2000) 225–271.

A copy of this paper is available on the second author's webpage here.

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