Homotopy groups of Hom complexes of graphs
| dc.creator | Dochtermann, Anton | |
| dc.date | 2007-05-18 | |
| dc.date | 2008-07-07 | |
| dc.date.accessioned | 2026-07-07T09:48:23Z | |
| dc.date.available | 2026-07-07T09:48:23Z | |
| dc.description | The notion of $\times$-homotopy from \cite{DocHom} is investigated in the context of the category of pointed graphs. The main result is a long exact sequence that relates the higher homotopy groups of the space $\Hom_*(G,H)$ with the homotopy groups of $\Hom_*(G,H^I)$. Here $\Hom_*(G,H)$ is a space which parametrizes pointed graph maps from $G$ to $H$ (a pointed version of the usual $\Hom$ complex), and $H^I$ is the graph of based paths in $H$. As a corollary it is shown that $π_i \big(\Hom_*(G,H) \big) \cong [G,Ω^i H]_{\times}$, where $ΩH$ is the graph of based closed paths in $H$ and $[G,K]_{\times}$ is the set of $\times$-homotopy classes of pointed graph maps from $G$ to $K$. This is similar in spirit to the results of \cite{BBLL}, where the authors seek a space whose homotopy groups encode a similarly defined homotopy theory for graphs. The categorical connections to those constructions are discussed. | |
| dc.description | 20 pages, 6 figures, final version, to be published in J. Combin. Theory Ser. A | |
| dc.identifier | https://arxiv.org/abs/0705.2620 | |
| dc.identifier | http://arxiv.org/abs/0705.2620 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164193 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Topology | |
| dc.subject | 05C15, 55P15, 57M15 | |
| dc.title | Homotopy groups of Hom complexes of graphs | |
| dc.type | text |