PreprintCC BY 4.0arXiv
Equivariant persistence topological complexity
Abstract
We introduce equivariant persistent analogues of Lusternik-Schnirelmann category, topological complexity, cup length, and zero-divisors cup length for persistent spaces with group actions, and establish their stability. In particular, we investigate their behavior under equivariant interleavings and obtain bounds for the corresponding erosion distances. For Vietoris--Rips filtrations of compact metric spaces equipped with compatible group actions, we relate the erosion distances between the resulting equivariant persistent invariants to appropriate equivariant versions of the Gromov-Hausdorff distance.
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BibTeX
@misc{daundkar2026equivariant,
title = {{Equivariant persistence topological complexity}},
author = {Navnath Daundkar and Ankur Sarkar and Bittu Singh},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29759},
eprint = {2609.29759},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29759},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Equivariant persistence topological complexity
AU - Navnath Daundkar
AU - Ankur Sarkar
AU - Bittu Singh
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29759
UR - https://arxiv.org/abs/2609.29759
AB - We introduce equivariant persistent analogues of Lusternik-Schnirelmann category, topological complexity, cup length, and zero-divisors cup length for persistent spaces with group actions, and establish their stability. In particular, we investigate their behavior under equivariant interleavings and obtain bounds for the corresponding erosion distances. For Vietoris--Rips filtrations of compact metric spaces equipped with compatible group actions, we relate the erosion distances between the resulting equivariant persistent invariants to appropriate equivariant versions of the Gromov-Hausdorff distance.
ER -