# Žiga Virk: On the contractibility of the Rips complexes of ℤⁿ

Date of publication: 26. 5. 2024

Geometric topology seminar

Wednesday

29

May

Time:

10:15 - 11:45

Location:

Online

ID: 927 2980 9880

We will prove that the Rips complexes of $\mathbb{Z}^n$ are contractible for large parameters $r$ when using the word metric (i.e., as the Cayley graphs). The current bounds for the relevant scale parameters are derived from the Jung constants. We will explain the conjecture on how to obtain the optimal bounds for the scale parameters. The result is motivated by the geometric group theory, by the reconstruction results in topology, and by the stability theorems for persistent homology. Our approach is based on a novel concept of combinatorial topology: the local domination of a vertex in a simplicial complex.

Vljudno vabljeni! B. Gabrovšek and D. Repovš