Parallel transport of Hom-complexes and the Lovász conjecture
نویسنده
چکیده
The groupoid of projectivities, introduced by M. Joswig [17], serves as a basis for a construction of parallel transport of graph and more general Hom-complexes. In this framework we develop a general conceptual approach to the Lovász conjecture, recently resolved by E. Babson and D. Kozlov in [4], and extend their result from graphs to the case of simplicial complexes.
منابع مشابه
Combinatorial Groupoids, Cubical Complexes, and the Lovász Conjecture
A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like “holonomy”, “parallel transport”, “bundles”, “combinatorial curvature” etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. A new, holonomy-type invariant for cubical complexes is introduced, leading to a combinatorial “Theorema Egregium”...
متن کاملO ct 2 00 5 Combinatorial groupoids , cubical complexes , and the Lovász conjecture
A foundation is laid for a theory of combinatorial groupoids, allowing us to use concepts like “holonomy”, “parallel transport”, “bundles”, “combinatorial curvature” etc. in the context of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. A new, holonomy-type invariant for cubical complexes is introduced, leading to a combinatorial “Theorema Egregium”...
متن کاملSimple 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...
متن کاملar X iv : m at h / 04 02 39 5 v 3 [ m at h . C O ] 1 8 Ju l 2 00 5 PROOF OF THE LOVÁSZ CONJECTURE
To any two graphs G and H one can associate a cell complex Hom (G,H) by taking all graph multihomorphisms from G to H as cells. In this paper we prove the Lovász Conjecture which states that if Hom (C2r+1, G) is k-connected, then χ(G) ≥ k + 4, where r, k ∈ Z, r ≥ 1, k ≥ −1, and C2r+1 denotes the cycle with 2r + 1 vertices. The proof requires analysis of the complexes Hom (C2r+1,Kn). For even n,...
متن کاملPROOF OF THE LOVÁSZ CONJECTURE 967 If φ ∈
To any two graphs G and H one can associate a cell complex Hom (G,H) by taking all graph multihomomorphisms from G to H as cells. In this paper we prove the Lovász conjecture which states that if Hom (C2r+1, G) is k-connected, then χ(G) ≥ k + 4, where r, k ∈ Z, r ≥ 1, k ≥ −1, and C2r+1 denotes the cycle with 2r+1 vertices. The proof requires analysis of the complexes Hom (C2r+1,Kn). For even n,...
متن کامل