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On the Simple ℤ2-homotopy Types of Graph Complexes and Their Simple ℤ2-universality
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- Journal:
- Canadian Mathematical Bulletin / Volume 51 / Issue 4 / 01 December 2008
- Published online by Cambridge University Press:
- 20 November 2018, pp. 535-544
- Print publication:
- 01 December 2008
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- Article
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We prove that the neighborhood complex
$\text{N}\left( G \right)$, the box complex 
$\text{B}\left( G \right)$, the homomorphism complex
$\text{Hom}\left( {{K}_{2}},\,G \right)$
and the Lovász complex 
$\text{L}\left( G \right)$ have the same simple
${{\mathbb{Z}}_{2}}$
-homotopy type in the sense of Whitehead. We show that these graph complexes are simple
${{\mathbb{Z}}_{2}}$
-universal.
