112,420 research outputs found
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 -module . 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
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