Decomposing Simplicial Complexes - Without Losing Pieces

Offered By: Applied Algebraic Topology Network via YouTube

Course Description

Overview

Explore the intricacies of decomposing simplicial complexes in this 48-minute lecture by Francesca Tombari from the Applied Algebraic Topology Network. Delve into the challenges of maintaining homotopy type during decomposition and reassembly, and discover how obstruction complexes can provide insights into these changes. Learn about the relationship between a simplicial complex's homotopy type and its decompositions, with practical demonstrations using Vietoris-Rips complexes. Covering topics from introductory examples to the general case and applications, gain a comprehensive understanding of this collaborative research involving Wojciech Chachólski, Martina Scolamiero, and Alvin Jin.

Syllabus

Introduction
Example
Decomposing
Setting
Main Theorem
Name Theorem
Questions
General case
Applications

Taught by

Applied Algebraic Topology Network

Related Courses

Vietoris-Rips Complexes of Hypercube Graphs
Applied Algebraic Topology Network via YouTube Ulrich Bauer - Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Rips Filtrations
Applied Algebraic Topology Network via YouTube Johnathan Bush - Maps of Čech and Vietoris–Rips Complexes into Euclidean Spaces
Applied Algebraic Topology Network via YouTube Henry Adams - Vietoris-Rips Complexes of Hypercube Graphs
Applied Algebraic Topology Network via YouTube Star Clusters in Clique Complexes and the Vietoris-Rips Complex of Planar Sets
Applied Algebraic Topology Network via YouTube