We study topological spaces with a distinguished set of paths, called directed paths. Since these directed paths are
generally not reversible, the directed homotopy classes of directed paths do not assemble into a groupoid, and
there is no direct analog of the fundamental group. However, they do assemble into a category, called the
fundamental category. We define models of the fundamental category, such as the fundamental bipartite graph,
and minimal extremal models which are shown to generalize the fundamental group. In addition, we prove
van Kampen theorems for subcategories, retracts, and models of the fundamental category.
Publié le : 2009-05-15
Classification:
Directed homotopy,
fundamental category,
van Kampen theorem,
$d$-space,
reflective subcategory,
coreflective subcategory,
past retract,
future retract,
extremal model,
fundamental bipartite graph,
55P99,
68Q85,
18A40,
18A30,
55U99
@article{1251832565,
author = {Bubenik, Peter},
title = {Models and van Kampen theorems for directed homotopy theory},
journal = {Homology Homotopy Appl.},
volume = {11},
number = {1},
year = {2009},
pages = { 185-202},
language = {en},
url = {http://dml.mathdoc.fr/item/1251832565}
}
Bubenik, Peter. Models and van Kampen theorems for directed homotopy theory. Homology Homotopy Appl., Tome 11 (2009) no. 1, pp. 185-202. http://gdmltest.u-ga.fr/item/1251832565/