Marco Radeschi
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Registered User
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Feb 1 |
awarded | ● Self-Learner |
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Feb 1 |
comment |
Submersions from compact flat manifold The point is: if $H^a(\tilde{N})$ is the highest nonzero cohomology group of $\tilde{N}$, and $H^b(F')$ the highest cohomology group of $F'$, then in the second page of the spectral sequence the term $E_2^{a,b}$ is nonzero, and no nonzero differentials land on it, or leave it. For this fact to be true it is important that both cohomologies of $F'$ and $\tilde{N}$ have only a finite number of nonzero cohomology group, so this passage does not apply in the situations you described. It follows that $E^{a,b}_2$ survives to the infinity page, and in particular $H^{a+b}(\tilde{M})\neq 0$. |
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Feb 1 |
comment |
Submersions from compact flat manifold Igor: As you say, you precompose the pullback with the universal cover. By the exact sequence in homotopy the fiber F′ is connected. What is not working in the second paragraph? |
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Jan 31 |
answered | Submersions from compact flat manifold |
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Jan 31 |
asked | Submersions from compact flat manifold |
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Jan 22 |
awarded | ● Yearling |
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Dec 17 |
revised |
Dense subgroups of Lie Groups edited title |
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Dec 17 |
comment |
Dense subgroups of Lie Groups @Misha: thanks for the explanation. One possible concept of complexity is the growth of H. I am trying to understand what kind of compact manifolds can admit H as fundamental group (or a quotient of it). |
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Dec 17 |
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Dense subgroups of Lie Groups @Yves: you are right, I meant finitely generated dense subgroup, without "discrete". |
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Dec 17 |
comment |
Dense subgroups of Lie Groups @Ryan, Yves: I edited my question, I hope it makes more sense now... |
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Dec 17 |
revised |
Dense subgroups of Lie Groups clearified the question |
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Dec 17 |
asked | Dense subgroups of Lie Groups |
