Arboricity, Dimension, Category
We aim to show that the Lusternik-Schnirelmann category of a graph is bound by the augmented dimension. We can try to prove this by using tree coverings and so look at arboricity.
Tag: graphs
Group Extensions and Naturalness
A bit about group theory triggered by the observation that some of the non-natural groups are non-simple groups which do not split. The later problem is a central issue in the classification problem of finite groups. While the finite simple groups have been classified in a monster effort and finitalized …
Graphs, Groups and Geometry
A bit more update on the project of natural spaces. Which groups are natural, which metric spaces are natural, which graphs are natural?
Mickey Mouse Sphere Theorem
The Mickey mouse theorem assures that a connected positive curvature graph of positive dimension is a sphere.
The Hydrogen Relation
For a one-dimensional simplicial complex, the sign less Hodge operator can be written as L-g, where g is the inverse of L. This leads to a Laplace equation shows solutions are given by a two-sided random walk.
Strong Ring of Simplicial Complexes
The strong ring is a category of geometric objects G which are disjoint unions of products of
simplicial complexes. Each has a Dirac operator D and a connection operator L. Both are related in
various ways to topology.