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.