Globular subdivisions are dihomotopy equivalences

TL;DR

This paper proves that globular subdivisions of multipointed d-spaces preserve dihomotopy types, ensuring consistent homological and homotopical properties across subdivisions.

Contribution

It establishes that globular subdivisions induce dihomotopy equivalences, linking subdivision processes to invariance in flows and homology theories.

Findings

Globular subdivisions lead to dihomotopy equivalences.

Flows from related multipointed d-spaces have isomorphic homology.

Underlying homotopy types are preserved under subdivisions.

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.