On ${\ell }_p$-Vietoris-Rips complexes

Sergei O. Ivanov, Xiaomeng Xu

We study the concepts of the ${\ell }_p$-Vietoris-Rips simplicial set and the ${\ell }_p$-Vietoris-Rips complex of a metric space, where $1\le p\le \infty .$ This theory unifies two es…