ar X iv : m at h / 03 10 05 6 v 3 [ m at h . C O ] 2 6 A ug 2 00 4 COMPLEXES OF GRAPH HOMOMORPHISMS

ar X iv : m at h / 03 10 05 6 v 2 [ m at h . C O ] 5 M ay 2 00 4 COMPLEXES OF GRAPH HOMOMORPHISMS

Hom (G,H) is a polyhedral complex defined for any two undirected graphs G and H. This construction was introduced by Lovász to give lower bounds for chromatic numbers of graphs. In this paper we initiate the study of the topological properties of this class of complexes. We show that Hom (K2, Kn) is a boundary complex of a polytope, on which the natural Z2-action on the first argument, induces ...

ar X iv : m at h / 03 11 05 9 v 1 [ m at h . O A ] 5 N ov 2 00 3 ON THE ASYMPTOTIC TENSOR NORM

We introduce a new asymptotic one-sided and symmetric tensor norm, the latter of which can be considered as the minimal tensor norm on the category of separable C *-algebras with homotopy classes of asymptotic homomorphisms as morphisms. We show that the one-sided asymptotic tensor norm differs in general from both the minimal and the maximal tensor norms and discuss its relation to semi-invert...

ar X iv : m at h / 03 05 20 7 v 4 [ m at h . D S ] 6 M ay 2 00 6 Lipschitz Flow - box Theorem

A generalization of the Flow-box Theorem is proven. The assumption of a C vector field f is relaxed to the condition that f be locally Lipschitz. The theorem holds in any Banach space.

ar X iv : m at h / 05 02 57 3 v 7 [ m at h . A G ] 8 A ug 2 00 6 ON DEFORMATIONS OF FLAG MANIFOLDS WITH

Any (global) kähler deformation of a flag manifold F with b2 = 1 is biholomorphic to F .

ar X iv : h ep - p h / 06 08 05 0 v 1 4 A ug 2 00 6 Percolation and high energy cosmic rays above 10 17 eV