Category: <span>simplicial complex</span>

The most general finite geometric structure

Delta sets are very general. They include simplicial complexes, open sets in simplicial complexes, quotients of simplicial complexes, quivers and so multi-graphs or simply hypergraphs, sets of sets. For the later, the geometry is not that interesting in general. As for quivers, the associated delta set is one dimensional only …

Geometry of Delta Sets

Historically, geometry started in Euclidean spaces. There was no concept of coordinate when Euclid wrote the “elements”. Using “points” and “lines” as building blocks and some axioms, the reader there is lead to quantitative concepts like “length”, “angle” or “area” and many propositions and theorem. Only with Descartes, the concept …

Arnold’s Theme

Here are some links to the articles mentioned in the talk: It surprisingly often happens that a big conjecture tumbles at around the same time. In the case of the Arnold conjecture, several approaches, spear headed by Conley-Zehnder, Eliashberg and Floer have reached the goal. But also almost always with …

Lagrange Riddle

In the program to get rid of any notion of infinity, one necessarily has to demonstrate that very classical and entrenched notions like topics appearing in a contemporary multi-variable calculus course can be replaced and used. Artificial discretisations do not help much in that; they serve as numerical schemes but …

A multi-particle energy theorem

A finite abstraact simplicial complex or a finite simple graph comes with a natural finite topological space. Some quantities like the Euler characteristic or the higher Wu characteristics are all topological invariants. One can also reformulate the Lefschetz fixed point theorem for continuous maps on finite topological spaces.