Tags » Simplicial Complex

The Čech Complex and the Vietoris-Rips Complex

It’s about time we got back to computational topology. Previously in this series we endured a lightning tour of the fundamental group and homology, then we saw… 1,762 more words


Simplicial Complex.

In mathematics, a simplicial complex is a topological space of a certain kind, constructed by “gluing together” points, line segments, triangles, and their n-dimensional counterparts. Basically from what I understand its a way of creating space out of simplexes. 87 more words


Representing an Abstract Simplicial Complex in Python

What’s an abstract simplicial complex?

So what is an abstract simplicial complex? It is a collection of finite sets that are closed under taking subsets.  1,370 more words


Numerical work with sage 4 - All possible triangulations of a simplicial complex using pachner moves

So what I’ve been able to do using sagemath is triangulate a simplicial complex using Pachner moves. The complete set of all possible triangulations can be recorded, saved and plotted in 3d using jmol. 75 more words

Special Unitary Group

Homology Theory — A Primer

This series on topology has been long and hard, but we’re are quickly approaching the topics where we can actually write programs. For this and… 3,576 more words


A Bosuk-Ulam-kind theorem for simplexes

This little note came out of a lunch discussion with NYU grad student Alfredo Hubard earlier this week. I think the problem-solving process was quite amusing hence worth shearing. 796 more words

Lecture 8a. A primer on simplicial complexes and collapsibility

Before we can apply more advanced fixed point theorems to the Evasiveness Conjecture, we need a little background on simplicial complexes, and everything starts with… 677 more words