ar X iv : c on d - m at / 0 30 10 15 v 1 2 J an 2 00 3 Topology of the World Trade Web

ar X iv : 0 90 8 . 37 24 v 1 [ m at h . A T ] 2 6 A ug 2 00 9 ON THE NON - EXISTENCE OF ELEMENTS OF KERVAIRE INVARIANT ONE

We show that the Kervaire invariant one elements θj ∈ π2j+2−2S 0 exist only for j ≤ 6. By Browder’s Theorem, this means that smooth framed manifolds of Kervaire invariant one exist only in dimensions 2, 6, 14, 30, 62, and possibly 126. Except for dimension 126 this resolves a longstanding problem in algebraic topology.

ar X iv : c on d - m at / 0 30 50 15 v 1 1 M ay 2 00 3 Phase transitions , memory and frustration in a Sznajd - like model with synchronous updating

Equally it is not unusual to come across door-to-door sale agents working in couples rather than on an individual basis. In democratic electoral campaigns, small groups (typically couples) of political party activists may visit, door-to-door, potential electors and seek to gain their votes. Trade union movements often try to coordinate their actions in order to strengthen their position against...

ar X iv : 0 71 2 . 22 30 v 3 [ m at h . D G ] 6 M ar 2 00 8 η Forms and Determinant Lines

ar X iv : c on d - m at / 0 10 30 52 v 1 2 M ar 2 00 1 NMR Frequencies of a Splay Soliton in 3 He - A

Superfluid 3 He-A has domain-wall like structures, which are called solitons. We calculate numerically the structure of a splay soliton and study its effect on the NMR spectrum by calculating the frequency and the amplitude of the soliton peaks. We compare the results with experiments and discuss their implications on the basic parameters of 3 He.

ar X iv : m at h - ph / 0 30 70 15 v 1 8 J ul 2 00 3 Integrable geodesic flows on Riemannian manifolds : Construction and Obstructions ∗ Alexey

This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.