Activity for WheatWizardâ€
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Question | — |
Seeking a theorem about lattices I am looking for a reference on the following theorem, or an equivalent statement: > Let $\Lambda$ be an embedding of a free $\mathbb{Z}$-module in $\mathbb{R}^d$. If the rank of $\Lambda$ is greater than $d$ then $\Lambda$ is not discrete. I have proofs here and here, which both seem correct t... (more) |
— | 23 days ago |
| Question | — |
Does {7,4|3} have a realization on the Klein quartic? It was pointed out to me recently that the polyhedron {7,4|3} has the same automorphism group as the Klein quartic. Specifically {7,4|3} is: $\langle \rho0,\rho1,\rho2 \mid \rho0^2, \rho1^2, \rho2^2, (\rho0\rho2)^2, (\rho0\rho1)^7, (\rho1\rho2)^4, (\rho0\rho1\rho2\rho1)^3\rangle$ Naturally t... (more) |
— | about 2 months ago |
| Question | — |
Is there a $(n_3)$ configuration which is not self-dual? Coxeter points out that for a self-dual configuration $(mc,nd)$ it must be that $m=n$ and $c=d$, so we may abbreviate it $(mc)$. However I'm interested in the other direction of this implication, i.e. is there a configuration $(mc,mc)$ which is not self-dual? For $c=2$ there is none. All polygons ... (more) |
— | 5 months ago |
| Question | — |
Is the nth Betti number determined by orientability? I'm interested in a proof of the following claim: > If $M$ is a connected $n$-dimensional compact manifold then the $n$th Betti number, $\betan(M) = 1$ if $M$ is orientable and $\betan(M) = 0$ otherwise. This claim seems true since it basically says that orientable manifolds have some sort of "... (more) |
— | 6 months ago |
| Question | — |
Proving that this relation implies another relation on the Coxeter group [4,3,3,4]. I have a group with five generators $\sigmai$, and the following relations: \begin{split} \sigmai^2 = \varepsilon \\ |i-j| \neq 1 \implies (\sigmai\sigmaj)^2 = \varepsilon \\ (\sigma0\sigma1)^4 = \varepsilon \\ (\sigma1\sigma2)^3 = \varepsilon \\ (\sigma2\sigma3)^3 = \varepsilon \\ (\sigma3\... (more) |
— | 10 months ago |
| Question | — |
What is special about the 11-cell and 57-cell? Reading about the 11-cell and 57-cell I find two facts implied often: - They are particularly notable among the abstract regular 4-polytopes. - They are related to each other. I'll establish why I think they are notable: - Both polytopes are notable enough to have their own articles on Wikipedi... (more) |
— | 11 months ago |