bio | website | |
---|---|---|
location | University of Pennsylvania, Philadelphia | |
age | 30 | |
visits | member for | 4 years, 8 months |
seen | 17 hours ago | |
stats | profile views | 730 |
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 |
comment |
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. |
Oct 29 |
asked | (Non)-exoticness of a diffeomorphism of a sphere |
Oct 15 |
comment |
Euler characteristic and universal cover
Hi Johannes! actually, my problem is that $\tilde{M}$ retracts to a lie group, but is not one. in particular, i don't see how i can make $\pi(M)$ act on the retraction, in a free fashion |
Oct 15 |
comment |
Euler characteristic and universal cover
Mark, thanks a lot for this! Two questions though: 1) For which groups does this work? from the other comments, i seem to understand that it holds for $\pi$ finitely presented, is this right? 2) I seem to understand that for the definition of $\chi(\tilde{M})$ you used the "usual" cohomology groups (as opposed to the compactly supported ones), is this correct? again, thank so much! |