Skip to main content

All Questions

Filter by
Sorted by
Tagged with
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 $\...
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 $p_i$ ...
0 votes
1 answer
308 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 ...
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 ...
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 $\...
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, ...
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-...