Globular subdivisions are dihomotopy equivalences
Algebraic Topology
2026-01-30 v3 Category Theory
Abstract
We prove that any globular subdivision of multipointed -spaces gives rise to a dihomotopy equivalence between the associated flows. As a straightforward application, the flows associated to two multipointed -spaces related by a finite zigzag of globular subdivisions have isomorphic branching and merging homology theories and isomorphic underlying homotopy types.
Cite
@article{arxiv.2502.11773,
title = {Globular subdivisions are dihomotopy equivalences},
author = {Philippe Gaucher},
journal= {arXiv preprint arXiv:2502.11773},
year = {2026}
}
Comments
45 pages, 5 figures; v2 : proof of Theorem 8.9 simplified thanks to the new Proposition 8.8; many other proofs expanded; an appendix about the underlying space functor; v3: minor changes