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Feb
2 |
comment |
Hausdorff limits of fibers of affine maps
Given subsets $X,Y$ of a metric space $Z$, the Hausdorff distance $d_H(X,Y)$ is the infimum number $r$ such that $X$ is contained in the $r$-ball around $Y$, and vice versa. For example, two concentric circles in the plane, of radii $a$ and $b$, have Hausdorff distance $|b-a|$. |
Jan
28 |
asked | Hausdorff limits of fibers of affine maps |
Feb
22 |
awarded | Popular Question |
Jul
2 |
awarded | Curious |
Mar
23 |
comment |
Relative Serre spectral sequences?
Thank you very much for the references! It's exactly what I was looking for. |
Mar
23 |
accepted | Relative Serre spectral sequences? |
Mar
23 |
asked | Relative Serre spectral sequences? |
Feb
1 |
awarded | Self-Learner |
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 $H^{a+b}(\tilde{M})\neq 0$. |
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? |
Jan
31 |
answered | Submersions from compact flat manifold |
Jan
31 |
asked | Submersions from compact flat manifold |
Jan
22 |
awarded | Yearling |
Dec
17 |
revised |
Dense subgroups of Lie Groups
edited title |
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). |
Dec
17 |
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Dense subgroups of Lie Groups
@Yves: you are right, I meant finitely generated dense subgroup, without "discrete". |
Dec
17 |
comment |
Dense subgroups of Lie Groups
@Ryan, Yves: I edited my question, I hope it makes more sense now... |
Dec
17 |
revised |
Dense subgroups of Lie Groups
clearified the question |
Dec
17 |
asked | Dense subgroups of Lie Groups |
Oct
29 |
comment |
(Non)-exoticness of a diffeomorphism of a sphere
Hi Ryan, thanks for the answer first of all. By torus i really meant $(S^1)^n$, even though I didn't say how that came up. I thought it was going to make the question heavier, and all I really wanted was to get to question 3. |