2 5 M ay 2 00 4 The cardinal characteristic for relative γ - sets

ar X iv : h ep - p h / 04 05 03 9 v 1 5 M ay 2 00 4 η , η ′ → π + π − γ with coupled channels

ar X iv : m at h / 04 01 30 5 v 2 [ m at h . G R ] 2 7 M ay 2 00 5 Closed subgroups of the infinite symmetric group

Let S = Sym(Ω) be the group of all permutations of a countably infinite set Ω, and for subgroups G1, G2 6 S let us write G1 ≈ G2 if there exists a finite set U ⊆ S such that 〈G1 ∪ U 〉 = 〈G2 ∪ U 〉. It is shown that the subgroups closed in the function topology on S lie in precisely four equivalence classes under this relation. Which of these classes a closed subgroup G belongs to depends on whic...

ar X iv : m at h / 05 05 24 4 v 1 [ m at h . G T ] 1 2 M ay 2 00 5 WORD HYPERBOLIC EXTENSIONS OF SURFACE GROUPS

Let S be a closed surface of genus g ≥ 2. A finitely generated group Γ S is an extension of the fundamental group π 1 (S) of S if π 1 (S) is a normal subgroup of Γ S. We show that the group Γ S is hyperbolic if and only if the orbit map for the action of the quotient group Γ = Γ S /π 1 (S) on the complex of curves is a quasi-isometric embedding.

m at h . A T ] 2 6 M ay 2 00 5 Chromatic numbers , morphism complexes , and Stiefel - Whitney characteristic classes . Dmitry N . Kozlov

ar X iv : 0 70 5 . 24 04 v 1 [ m at h . C O ] 1 6 M ay 2 00 7 Misère Quotients for

This appendix contains detailed solutions to many of the games discussed in Appendix A. Figure 1 summarizes the status of every octal game with at most three code digits. For each game Γ, the chart indicates whether Γ is tame or wild, and whether its normaland/or misère-play solution is known. Figures 2 and 4 present complete solutions to wild twoand three-digit octal games with relatively simp...