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Sean Lawton
Sean Lawton
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p-local space vs p-completion.

I haveam having some trouble to understandunderstanding the difference between the p$p$-completion and pa $p$-local space. if

If $X$ a simply connected spaces such thatspace has all higher homotopy groups are finitely generated groups, then the p$p$-local approximation $X\rightarrow L_{p}X$ coincides with the $p$-completion $X_{p}^{\wedge}$. Is itthis correct? 

Now if $X$ is not simply connected such that the fundamental group is abelian, do we have that $ L_{p}X \simeq X_{p}^{\wedge}$.?

I think it is true if $X$ is a circle, more precisely, $S^{1\wedge}_{p}\sim L_{p}S^{1}\sim K(\mathbf{Z}_{p}^{\wedge},1)$. Am I wrong ?

p-local space vs p-completion.

I have some trouble to understand the difference between the p-completion and p-local space. if $X$ a simply connected spaces such that all higher homotopy groups are finitely generated groups then the p-local approximation $X\rightarrow L_{p}X$ coincides with the $p$-completion $X_{p}^{\wedge}$. Is it correct? Now if $X$ is not simply connected such that the fundamental group is abelian do we have that $ L_{p}X \simeq X_{p}^{\wedge}$. I think it is true if $X$ is a circle, more precisely $S^{1\wedge}_{p}\sim L_{p}S^{1}\sim K(\mathbf{Z}_{p}^{\wedge},1)$. Am I wrong ?

p-local space vs p-completion

I am having some trouble understanding the difference between the $p$-completion and a $p$-local space.

If $X$ a simply connected space has all higher homotopy groups finitely generated, then the $p$-local approximation $X\rightarrow L_{p}X$ coincides with the $p$-completion $X_{p}^{\wedge}$. Is this correct? 

Now if $X$ is not simply connected such that the fundamental group is abelian, do we have that $ L_{p}X \simeq X_{p}^{\wedge}$?

I think it is true if $X$ is a circle, more precisely, $S^{1\wedge}_{p}\sim L_{p}S^{1}\sim K(\mathbf{Z}_{p}^{\wedge},1)$. Am I wrong ?

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sphere
sphere
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p-local space vs p-completion.

I have some trouble to understand the difference between the p-completion and p-local space. if $X$ a simply connected spaces such that all higher homotopy groups are finitely generated groups then the p-local approximation $X\rightarrow L_{p}X$ coincides with the $p$-completion $X_{p}^{\wedge}$. Is it correct? Now if $X$ is not simply connected such that the fundamental group is abelian do we have that $ L_{p}X \simeq X_{p}^{\wedge}$. I think it is true if $X$ is a circle, more precisely $S^{1\wedge}_{p}\sim L_{p}S^{1}\sim K(\mathbf{Z}_{p}^{\wedge},1)$. Am I wrong ?