4 papers
The homotopy types of directed path and trace spaces
Philippe Gaucher
We construct a saturated directed space with a Hausdorff -generated underlying space and two distinct points such that the trace space between them is homeomorphic to a square,…
Branching space of precubical set
Philippe Gaucher
Using the notion of short natural directed path, we introduce the homotopy branching space of a precubical set. It is unique only up to homotopy equivalence. We prove that, for any…
Branching spaces of multipointed d-spaces
Philippe Gaucher
Using the notion of a short directed path, we introduce the branching space of a multipointed d-space. We prove that for any q-cofibrant multipointed d-space, it is homeomorphic to…
Globular subdivisions are dihomotopy equivalences
Philippe Gaucher
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 a…