All Questions
7 questions
6
votes
1
answer
539
views
Proofs of Euler's characteristic formula for n-Dim polytopes
Twenty proofs of Euler's formula V - E + F - 1 = 1, which applies to convex polyhedrons, i.e., 3-dimensional polytopes, are presented at the Geometry Junkyard.
I'm interested in proofs of the more ...
- 10.5k
5
votes
1
answer
368
views
Six people standing on earth
Consider 6 people $p_i$, $i=1,\dots 6$, standing on a sphere $S^2$. We label the positions of these people by $p_i$ again. Suppose no pair of these points $p_i$ are antipodal. At each point $p_i$ ...
- 434
5
votes
0
answers
604
views
The twisted kiss of the curvaceous cubic and the staid tetrahedron (references)
(Migrated from MSE)
While investigating some operators, I came across some relations between the twisted cubic curve and the tetrahedron that link together some notions in differential geometry, ...
- 10.5k
4
votes
1
answer
210
views
A map on Grassmannian
Let $G=SL_{2n}$ and let $\sigma:G \to G$ be defined by $\sigma (A)= E(A^t)^{-1}E^{-1}$, where $E=antidiag(1,1, ... ,1,-1,-1,...,-1)$. Then the maximal parabolic associated to the simple root $\...
- 121
3
votes
1
answer
542
views
A good vector field to calculate the Euler's number of a compact differentiable manifold
Given a triangulation of a compact, orientable and differentiable manifold $M^m$, it is possible to give a formula (in terms of real coordinates of the ambient space) for a vector field with only non-...
- 31
3
votes
0
answers
233
views
A bridge between the algebraic / differential geometry of $\frak{sl}_2(\mathbb{C})$ and the Sheffer-Appell calculus and combinatorics
In "Four examples of Beilinson-Bernstein localization", Anna Romanov introduces the basis
$m_k = \frac{(-1)^k}{k!} \partial^k \delta $
on p. 9, where $\partial$ is a partial derivative and $\...
- 10.5k
0
votes
1
answer
307
views
About Alexander method in mapping class group
The Alexander Method in Farb and Maraglit's "A Primer on Mapping Class Groups"
For a surface $S$ with marked points, we say that a collection $\left\{\gamma_{i}\right\}$ of curves and arcs ...
- 119