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If $G := \langle a_k : k \in \mathbb{Z} \rangle$ and $H:= \langle a_{k+1} - a_k : k \in\mathbb{Z} \rangle$, Prove that $G/H \cong \mathbb{Z}$

There is a surjective homomorphism $G\to\mathbb Z$ sending $\sum_{k\in\mathbb Z}N_ka_k$ (where all but finitely many $N_k$ are zero) to $\sum_{k\in\mathbb Z}N_k$. The kernel consists of $\sum_{k\in\...
Kenta S's user avatar
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2 votes
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Homology of mapping telescope calculation

As ronno points out in the comments, what you wrote is not correct: each $X_n$ deformation retracts onto $S^1$, so $H_1(X_n) \cong \mathbb{Z}$. The way mapping telescope computations like this work is ...
Ben Steffan's user avatar
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1 vote
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Is there any Kunneth formula for the Lie algebra cohomology with coefficients in the adjoint representation

I only know K√ľnneth formulas for the trivial module $\Bbb C$. But one could also use the Hochschild-Serre formula for the semidirect product $\mathfrak{g}=\mathfrak{h}\ltimes \mathfrak{a}$, which ...
Dietrich Burde's user avatar

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