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On the Simple $\Z_2$-homotopy Types of Graph Complexes and Their Simple $\Z_2$-universality

Published:2008-12-01
Printed: Dec 2008
• Péter Csorba
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Abstract

We prove that the neighborhood complex $\N(G)$, the box complex $\B(G)$, the homomorphism complex $\Hom(K_2,G)$and the Lov\'{a}sz complex $\L(G)$ have the same simple $\Z_2$-homotopy type in the sense of Whitehead. We show that these graph complexes are simple $\Z_2$-universal.
 Keywords: graph complexes, simple $\Z_2$-homotopy, universality
 MSC Classifications: 57Q10 - Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc. [See also 19B28] 05C10 - Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 55P10 - Homotopy equivalences

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