The homotopy orbit spectrum for profinite groups

Let G be a profinite group. We define an S[[G]]-module to be a G-spectrum X that satisfies certain conditions, and, given an S[[G]]-module X, we define the homotopy orbit spectrum X_{hG}. When G is countably based and X satisfies a certain finiteness condition, we construct a homotopy orbit spectral sequence whose E_2-term is the continuous homology of G with coefficients in the graded profinite $\hat{\mathbb{Z}}[[G]]$-module $\pi_\ast(X)$. Let G_n be the extended Morava stabilizer group and let E_n be the Lubin-Tate spectrum. As an application of our theory, we show that the function spectrum F(E_n,L_{K(n)}(S^0)) is an S[[G_n]]-module with an associated homotopy orbit spectral sequence.Comment: 13 page

Homotopy fixed points for profinite groups emulate homotopy fixed points for discrete groups

If K is a discrete group and Z is a K-spectrum, then the homotopy fixed point spectrum Z^{hK} is Map_*(EK_+, Z)^K, the fixed points of a familiar expression. Similarly, if G is a profinite group and X is a discrete G-spectrum, then X^{hG} is often given by (H_{G,X})^G, where H_{G,X} is a certain explicit construction given by a homotopy limit in the category of discrete G-spectra. Thus, in each of two common equivariant settings, the homotopy fixed point spectrum is equal to the fixed points of an explicit object in the ambient equivariant category. We enrich this pattern by proving in a precise sense that the discrete G-spectrum H_{G,X} is just "a profinite version" of Map_*(EK_+, Z): at each stage of its construction, H_{G,X} replicates in the setting of discrete G-spectra the corresponding stage in the formation of Map_*(EK_+, Z) (up to a certain natural identification).Comment: 16 pages, the tex file uses the style file of the New York Journal of Mathematic

On asymptotic dimension of groups

We prove a version of the countable union theorem for asymptotic dimension and we apply it to groups acting on asymptotically finite dimensional metric spaces. As a consequence we obtain the following finite dimensionality theorems. A) An amalgamated product of asymptotically finite dimensional groups has finite asymptotic dimension: asdim A *_C B < infinity. B) Suppose that G' is an HNN extension of a group G with asdim G < infinity. Then asdim G'< infinity. C) Suppose that \Gamma is Davis' group constructed from a group \pi with asdim\pi < infinity. Then asdim\Gamma < infinity.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-4.abs.htm

Fabrication of uniaxial filament-reinforced epoxy tubes for structural application

Filament reinforced composite materials have high strength, high stiffness and low density. Tubes fabricated from process described have advantages of having smooth inner and outer surfaces, lower dimensional variation than tolerances set for extruded aluminum tubing and void free composites