Colloquium: "Simplicial homology, part I" by Dr. Guilherme Sadovski

Speaker: Dr. Sadovski is a member of this unit (visit his page)

Abstract: Part I of IV in our series will consist of introducing the building blocks of simplicial homology: the n-simplexes. These are pieces of${\displaystyle \mathbb {R} }$ \(\mathbb{R}^n\) which are nothing but our familiar notion of a triangle generalized to n-dimensions. We will define how these pieces might intersect with each other in order to form the so-called simplicial complex. A polyhedron will be defined as the union of all these pieces. Finally, a triangulation of a topological space X, if exists, will be defined as a pair \((K,\phi)\) which consists of a polyhedron K and a homoeomorphism \(ϕ : K → X\).