Globular subdivisions are dihomotopy equivalences

Abstract

We prove that any globular subdivision of multipointed $d$-spaces gives rise to a dihomotopy equivalence between the associated flows. As a straightforward application, the flows associated to two multipointed $d$-spaces related by a finite zigzag of globular subdivisions have isomorphic branching and merging homology theories and isomorphic underlying homotopy types.

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