Some Remarks on the Cohomology of the Vietoris-Rips Complex of a Hypercube Graph
Speaker:
Martin Bendersky, Hunter College of CUNY
Date and Time:
Monday, July 29, 2024 - 10:15am to 11:00am
Location:
Fields Institute, Room 230
Abstract:
We bring in the techniques of the moment angle complex of a simplicial complex, the independence complexes of a graph and the notion of total dominating sets of a graph to bear on the question of the cohomology of the Vietoris-Rips complexes $VR(Q_{n}; r)$ of an $n$-hypercube graph. We obtain bounds for the connectivity and co-connectivity of $VR(Q_{n}; r)$ for an arbitrary $n$-dimension hypercube and at all scale parameters $r$. This joint work with Jelena Grbic.