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comment Most interesting mathematics mistake?
@JimConant: Yes, of course.
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comment What is (co)homology, and how does a beginner gain intuition about it?
@DanielMcLaury Hatcher's "Algebraic Topology" has a section on the "Dold-Thom theorem" as section 4.K. Look there.
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comment Action of the mapping class group on separating spheres in a connected sum of aspherical 3-manifolds
@RyanBudney I might be misconstruing your comment, but I think you are describing the generators of $Aut(\pi_1(M))$, like on page 9 of the Hatcher-Wahl paper arxiv.org/abs/0709.2173. The map $\Gamma \to Aut(\pi_1(M))$ has a kernel (also described there). I am not sure how all of those things act on $\pi_2(M)$. Even with the elements of $\Gamma$ whose action I understand, I'm not sure whether there is some clever way to show that $2 \cdot [S_1] = 0 \in \pi_2(M)//\Gamma$ (the fact that $g \cdot [S_1] = 0$ was already a surprise to me).
May
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revised Action of the mapping class group on separating spheres in a connected sum of aspherical 3-manifolds
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May
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comment Action of the mapping class group on separating spheres in a connected sum of aspherical 3-manifolds
@user39082 Yes, I do. That is a very good point, thank you.
May
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revised Action of the mapping class group on separating spheres in a connected sum of aspherical 3-manifolds
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revised Action of the mapping class group on separating spheres in a connected sum of aspherical 3-manifolds
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May
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comment Action of the mapping class group on separating spheres in a connected sum of aspherical 3-manifolds
@user39082: The mapping class group includes an element that rotates the picture I drew by 90 degrees clockwise. This takes $S_1$ to $S_2$, and thus identifies them in $\pi_2(M)//\Gamma$.
May
15
answered How to prove the connected sum of two closed aspherical n-manfolds (n >2) is not asperical?
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revised Action of the mapping class group on separating spheres in a connected sum of aspherical 3-manifolds
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revised Action of the mapping class group on separating spheres in a connected sum of aspherical 3-manifolds
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