Branching space of multipointed d-space
Algebraic Topology
2026-02-05 v4 Category Theory
Abstract
Using the notion of short directed path, we introduce the branching space of a multipointed -space. We prove that for any q-cofibrant multipointed -space, it is homeomorphic to the branching space of the q-cofibrant flow obtained by applying the categorization functor. As an application, we deduce a purely topological proof of the invariance of the branching space and of the branching homology of cellular multipointed -spaces up to globular subdivision. By reversing the time direction, the same results are obtained for the merging space and the merging homology.
Keywords
Cite
@article{arxiv.2507.08377,
title = {Branching space of multipointed d-space},
author = {Philippe Gaucher},
journal= {arXiv preprint arXiv:2507.08377},
year = {2026}
}
Comments
25 pages. some material taken from arXiv:2502.11773 ; v2: some reorganization (the numbering of the theorems is modified); v3: fixes and improvements; v4: new introduction