Models and van Kampen theorems for directed homotopy theory

Details Models and van Kampen theorems for directed homotopy theory Models and van Kampen theorems for directed homotopy theory

2008-10-22

arxiv.org/abs/0810.4164v1

Homology, Homotopy and Applications, Vol. 11 (2009), No. 1, pp.185-202.

Mathematics

Algebraic Topology

20 pages, 10 figures

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Models and van Kampen theorems for directed homotopy theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Models and van Kampen theorems for directed homotopy theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Models and van Kampen theorems for directed homotopy theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-679912