Any finite group acts freely and homologically trivially on a product of spheres

The main theorem is that if K is a finite CW complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X x S^n for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial then so is the action on X x S^n. Unlu and Yalcin recently showed that for every finite group G, there is a finite CW complex K with fundamental group G which acts homologicially trivially on the universal cover of K. Thus every finite group acts smoothly, freely, and homologically trivially on a product of spheres.Comment: 11 pages. Final version. To appear in the Proceedings of the American Mathematical Societ

A two component link with Alexander polynomial one is concordant to the Hopf link

Four-dimensional surgery is used to show that a two component link with Alexander polynomial one is topologically concordant to the Hopf link.Comment: To appear in the Mathematical Proceedings of the Cambridge Philosophicial Societ

ENERGY REQUIREMENTS IN FOOD MARKETING

Energy needs of the various sectors of the food industry are outlined. Also, potential problems in meeting these needs are discussed.Resource /Energy Economics and Policy,

The topological K-theory of certain crystallographic groups

Let Gamma be a semidirect product of the form Z^n rtimes Z/p where p is prime and the Z/p-action on Z^n is free away from the origin. We will compute the topological K-theory of the real and complex group C*-algebra of Gamma and show that Gamma satisfies the unstable Gromov-Lawson-Rosenberg Conjecture. On the way we will analyze the (co-)homology and the topological K-theory of the classifying spaces BGamma and underbar{B}Gamma. The latter is the quotient of the induced Z/p-action on the torus T^n.Comment: 46 pages. Final version. Accepted for publication in the Journal of Noncommutative Geometr

There is no tame triangulation of the infinite real Grassmannian

We show that there is no triangulation of the infinite real Grassmannian of k-planes in R^\infty which is nicely situated with respect to the coordinate axes. In terms of matroid theory, this says there is no triangulation of the Grassmannian subdividing the matroid stratification. This is proved by an argument in projective geometry, considering a specific sequence of configurations of points in the plane.Comment: 11 page