ar X iv : m at h / 04 10 33 5 v 2 [ m at h . C O ] 3 1 Ja n 20 05 HIGHER CONNECTIVITY OF GRAPH COLORING COMPLEXES

ar X iv : m at h / 04 10 33 5 v 1 [ m at h . C O ] 1 4 O ct 2 00 4 HIGHER CONNECTIVITY OF GRAPH COLORING COMPLEXES SONJA

The main result of this paper is a proof of the following conjecture of Babson & Kozlov: Theorem. Let G be a graph of maximal valency d, then the complex Hom (G, Kn) is k-connected, whenever n ≥ d + k + 2. Here Hom (−,−) denotes the polyhedral complex introduced by Lovász to study the topological lower bounds for chromatic numbers of graphs. We will also prove, as a corollary to the main theore...

ar X iv : m at h - ph / 0 50 10 33 v 1 1 2 Ja n 20 05 Indefinite metric

ar X iv : m at h / 04 01 12 6 v 1 [ m at h . N T ] 1 3 Ja n 20 04 THREE LECTURES ON THE RIEMANN ZETA - FUNCTION

ar X iv : m at h / 03 10 33 9 v 1 [ m at h . C O ] 2 1 O ct 2 00 3 Box complexes , neighborhood complexes , and the chromatic number

Lovász’s striking proof of Kneser’s conjecture from 1978 using the Borsuk–Ulam theorem provides a lower bound on the chromatic number χ(G) of a graph G. We introduce the shore subdivision of simplicial complexes and use it to show an upper bound to this topological lower bound and to construct a strong Z2-deformation retraction from the box complex (in the version introduced by Matoušek and Zie...

ar X iv : m at h / 05 01 45 4 v 1 [ m at h . A G ] 2 5 Ja n 20 05 HIGHER NOETHER - LEFSCHETZ LOCI OF ELLIPTIC SURFACES

We calculate the dimension of the locus of elliptic surfaces over P 1 with a section and a given Picard number, in the corresponding moduli space.