DMS Topology Seminar

Speaker: Dr. Krystyna Kuperberg 

Title: The Vietoris complex

Abstract:  In 1927, Leopold Vietoris defined homology groups for arbitrary compact metric spaces. Soon after that Eduard Čech extended the definition to non-metric spaces. The chain complex defined by Vietoris gained a renewed attention some 60 years later in the work of Mikhael  (Misha) Gromov and became known as the Vietoris-Rips complex. The Vietoris complex is better suitable for applications than the Čech complex.

I shall give the basic definitions of the Vietoris complex. No prior knowledge is required, although it might be helpful to know the very basics of simplicial homology for finite complexes, i.e., compact polyhedra in the Euclidean space.