Homotopy Theory for Ordered Simplicial Complexes
Algebraic Topology
2026-05-18 v2
Abstract
We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a new model for the homotopy theory of spaces.
Cite
@article{arxiv.2509.22968,
title = {Homotopy Theory for Ordered Simplicial Complexes},
author = {Melissa Wei},
journal= {arXiv preprint arXiv:2509.22968},
year = {2026}
}
Comments
v2; final version to appear in Homology, Homotopy and Applications