Analog category and complexity
Algebraic Topology
2024-05-22 v2 Geometric Topology
Abstract
We study probabilistic variants of the Lusternik--Schnirelmann category and topological complexity, which bound the classical invariants from below. We present a number of computations illustrating both wide agreement and wide disagreement with the classical notions. In the aspherical case, where our invariants are group invariants, we establish a counterpart of the Eilenberg--Ganea theorem in the torsion-free case, as well as a contrasting universal upper bound in the finite case.
Cite
@article{arxiv.2401.15667,
title = {Analog category and complexity},
author = {Ben Knudsen and Shmuel Weinberger},
journal= {arXiv preprint arXiv:2401.15667},
year = {2024}
}
Comments
20 pages. To appear in SIAM Journal on Applied Algebra and Geometry. May differ slightly from published version