2009/06/22 by Terrence Bisson, Bisson, Terrence, Aristide Tsemo +1
Mathematics · #05C20 #05C38 #18F20 #55U35 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #math.AT #math.CT #msc:05C20 #msc:05C38 #msc:18F20 #msc:55U35
paper · pdf · doi:10.48550/arxiv.0906.4087
arxiv created 2009/06/25 · arxiv updated 2009/12/01
In this paper, we investigate the Quillen model structure defined by Bisson and Tsemo in the category of directed graphs Gph. In particular, we give a precise description of the homotopy category of graphs associated to this model structure. We endow the categories of N-sets and Z-sets with related model structures, and show that their homotopy categories are Quillen equivalent to the homotopy category Ho(Gph). This enables us to show that Ho(Gph) is equivalent to the category cZSet of periodic Z-sets, and to show that two finite directed graphs are almost-isospectral if and only if they are homotopy-equivalent in our sense.