Simple homotopy types of Hom-complexes, neighborhood complexes, Lovász complexes, and atom crosscut complexes
نویسندگان
چکیده
منابع مشابه
Simple Homotopy Types of Hom-complexes, Neighborhood Complexes, Lovász Complexes, and Atom Crosscut Complexes
In this paper we provide concrete combinatorial formal deformation algorithms, namely sequences of elementary collapses and expansions, which relate various previously extensively studied families of combinatorially defined polyhedral complexes. To start with, we give a sequence of elementary collapses leading from the barycentric subdivision of the neighborhood complex to the Lovász complex of...
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The notion of ×-homotopy from [Doca] 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 ). Here Hom∗(G,H) is a space which parameterizes pointed graph maps from G to H (a pointed version of the usual Hom complex), and H is the graph of based...
متن کاملHom complexes and homotopy in the category of graphs
We investigate a notion of ×-homotopy of graph maps that is based on the internal hom associated to the categorical product in the category of graphs. It is shown that graph ×homotopy is characterized by the topological properties of the Hom complex, a functorial way to assign a poset (and hence topological space) to a pair of graphs; Hom complexes were introduced by Lovász and further studied ...
متن کاملHom complexes and homotopy theory in the category of graphs
We investigate a notion of ×-homotopy of graph maps that is based on the internal hom associated to the categorical product in the category of graphs. It is shown that graph ×homotopy is characterized by the topological properties of the Hom complex, a functorial way to assign a poset (and hence topological space) to a pair of graphs; Hom complexes were introduced by Lovász and further studied ...
متن کاملHom Complexes of Set Systems
A set system is a pair S = (V (S),∆(S)), where ∆(S) is a family of subsets of the set V (S). We refer to the members of ∆(S) as the stable sets of S. A homomorphism between two set systems S and T is a map f : V (S) → V (T ) such that the preimage under f of every stable set of T is a stable set of S. Inspired by a recent generalization due to Engström of Lovász’s Hom complex construction, the ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2006
ISSN: 0166-8641
DOI: 10.1016/j.topol.2005.09.005