English

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.

Keywords

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

R2 v1 2026-07-01T05:59:58.687Z