Applications of closed models defined by counting to graph theory and topology

Tsemo Aristide

Abstract


In this paper, we define the notion of closed models defined by counting, and we compute their homotopy categories. We apply this construction to various categories of graphs. We show that there does not exist a closed model in the category of undirected graphs which characterizes the Ihara Zeta function in the sense that, a morphism $f:X\rightarrow Y$ is a weak equivalence for this model if and only if it induces a bijection between the sets of non degenerated cycles of $X$ and $Y$. Finally, we apply our construction to Galoisian complexes and dessins d'enfant.

Full Text: PDF

Published: 2017-02-18

How to Cite this Article:

Tsemo Aristide, Applications of closed models defined by counting to graph theory and topology, Algebra Letters, Vol 2017 (2017), Article ID 2

Copyright © 2017 Tsemo Aristide. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Algebra Letters

ISSN 2051-5502

Editorial Office: office@scik.org

Copyright ©2017 SCIK Publishing Corporation. All rights reserved.