Real Root Conjecture fails for five and higher dimensional spheres

A construction of convex flag triangulations of five and higher dimensional spheres, whose h-polynomials fail to have only real roots, is given. We show that there is no such example in dimensions lower than five. A condition weaker than realrootedness is conjectured and some evidence is providedComment: 15 pages, 1 figur

Euler characteristic of the configuration space of a complex

A closed form formula (generating function) for the Euler characteristic of the configuration space of $\scriptstyle n$ particles in a simplicial complex is given.Comment: 6 pages, no figure

Asymptotic dimension and uniform embeddings

We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The method allows to obtain the lower bound of the compression of the lamplighter group $Z\wr Z$, which has infinite asymptotic dimension.Comment: 17 pages, no figure

On the scattering length of the K^- d system

Multiple-scattering approximations to Faddeev calculations of the K^- d scattering length are reviewed and compared with published Kbar-N-N pi-Y-N fully reactive Faddeev calculations. A new multiple-scattering approximation which goes beyond the `fixed-center' assumption for the nucleons is proposed, aiming at accuracies of 5-10%. A precise value of the K^- d scattering length from the measurement of the K^- d 1s atomic level shift and width, planned by the DEAR/SIDDHARTA collaboration, plus a precise value for the K^- p scattering length by improving the K^- p atom measurements, are essential for extracting the K^- n scattering length, for resolving persistent puzzles in low-energy Kbar-N phenomenology and for extrapolating into Kbar-nuclear systems.Comment: Invited talk at MESON 2006, Krakow, June 2006. To be published in International Journal of Modern Physics A. Requires use of ws-ijmpa.cl

On approximation properties of semidirect products of groups

Let R be a class of groups closed under taking semidirect products with finite kernel and fully residually R-groups. We prove that R contains all R-by-{finitely generated residually finite} groups. It follows that a semidirect product of a finitely generated residually finite group with a surjunctive group is surjunctive. This remained unknown even for direct products of a surjunctive group with the integers Z.Comment: 6 pages, no figure