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I'm trying to find the fundamental group of the cone, and this question appear on my mind:

Since we can defined the cone as $CX=X\times I/I\times \{1\}$, what we can say about $CX$? If we know the fundamental group of $X$, what we can say about the fundamental group of $CX$? We can generalize this to any relation $\sim$ ? I saw in a pdf the author says $\pi_1(cone)=1$ what he means with that? he doesn't specify which kind of cone is. I think maybe he says the cone in $\mathbb R^3$.

I need help.

Thanks

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    $CX$ deformation retracts to a point, and hence is contractible. Thus $\pi_1(CX) = 1$.2012-11-25
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    @RafaelChavez Here is an explicit deformation retract: http://math.stackexchange.com/a/189989/382682012-11-26
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    @BenjaLim thank you, it helped a lot :)2012-11-26

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