Explore star clusters in clique complexes and the Vietoris-Rips complex of planar sets in this 50-minute conference talk by Jonathan Barmak. Delve into the concept of star clusters in simplicial complexes and their contractibility in clique complexes. Discover applications of this notion in studying homotopy invariants of independence complexes of graphs. Examine the Vietoris-Rips complex of planar sets, including its free fundamental group property and the conjecture about its homotopy type. Learn how star clusters can be utilized to obtain homotopy information of the Vietoris-Rips complex. The talk covers topics such as independence complexes of graphs, proofs, applications, nontrivial lower bounds, contractile subcomplexes, and concludes with questions and discussions on uniform bounds.
Star Clusters in Clique Complexes and the Vietoris-Rips Complex of Planar Sets
Applied Algebraic Topology Network via YouTube
Overview
Syllabus
Introduction
Independence complexes of graphs
Star clusters
Independence complexes
Proof
Applications
Other homotopic types
Nontrivial lower bounds
Contractile subcomplex
Questions
Uniform bound
Taught by
Applied Algebraic Topology Network
Related Courses
-
Henry Adams - Vietoris-Rips Complexes of Hypercube Graphs
-
Homotopical Decompositions of Simplicial and Vietoris Rips Complexes
-
Vietoris-Rips Complexes of Hypercube Graphs
-
Homotopy Types of Vietoris–Rips Complexes of Metric Gluings
-
The Vietoris Rips Complex of the Circle
-
Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius
