ar X iv : 0 70 6 . 13 26 v 3 [ m at h . M G ] 2 7 Fe b 20 09 THE OSCILLATION STABILITY PROBLEM FOR THE URYSOHN SPHERE : A COMBINATORIAL APPROACH

. M G ] 9 J un 2 00 7 THE OSCILLATION STABILITY PROBLEM FOR THE URYSOHN SPHERE : A COMBINATORIAL APPROACH

We study the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for ℓ 2 in the context of the Urysohn space U. In particular, we show that this problem reduces to a purely combinatorial problem involving a family of countable ultrahomogeneous metric spaces with finitely many distances.

. M G ] 1 2 O ct 2 00 7 THE OSCILLATION STABILITY PROBLEM FOR THE URYSOHN SPHERE : A COMBINATORIAL APPROACH

We study the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for ℓ 2 in the context of the Urysohn space U. In particular, we show that this problem reduces to a purely combinatorial problem involving a family of countable ultrahomogeneous metric spaces with finitely many distances.

ar X iv : 0 90 2 . 39 12 v 1 [ m at h . G R ] 2 3 Fe b 20 09 Brent Everitt The Combinatorial Topology

ar X iv : 0 90 2 . 32 39 v 1 [ m at h . D G ] 1 8 Fe b 20 09 Gauge theory in higher dimensions , II

ar X iv : m at h / 06 09 09 3 v 3 [ m at h . A G ] 2 1 Fe b 20 07 INVARIANTS OF NEWTON NON - DEGENERATE SURFACE SINGULARITIES

We recover the Newton diagram (modulo a natural ambiguity) from the link for any surface hypersurface singularity with non-degenerate Newton principal part whose link is a rational homology sphere. As a corollary, we show that the link determines the embedded topological type, the Milnor fibration, and the multiplicity of such a germ. This proves (even a stronger version of) Zariski's Conjectur...