Subject: Hopf
Date: 04 Nov 2002 08:23:19 +0000
From: nsthov01@newton.cam.ac.uk (M.A. Hovey)
To: dmd1@lehigh.edu
6 new papers this time, from Goerss-Henn-Mahowald-Rezk, 2 from
Kadeishvili-Saneblidze, Klein, Levi-Oliver, and
Rodriguez-Scherer-Viruel. Also, I fixed a stupid error in my paper
Hovey/comodule so if you downloaded that before Oct. 15, you might want
to download a new copy.
Mark Hovey
New papers appearing on hopf between 10/07/02 and 11/04/02
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Goerss-Henn-Mahowald-Rezk/ghmr-14-10-02
Title: A resolution of the K(2)-local sphere
Authors: Paul Goerss, Hans-Werner Henn, Mark Mahowald and Charles Rezk
Adresses:
Northwestern University, Universite Louis Pasteur, Northwestern University,
University of Illinois at Urbana
ABSTRACT
At the prime p=3, we write the spectrum L_{K(2)}S^0 as the inverse limit
of a short tower of fibrations where the fibers are (suspensions of)
explicit homotopy fixed point spectra E_2^{hF} with F a finite subgroup
of the Morava stabilizer group.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Kadeishvili-Saneblidze/cubmodel
A cubical model for a fibration
by
TORNIKE KADEISHVILI AND SAMSON SANEBLIDZE
In the paper the notion of truncating twisting function $\tau
:X\to Q$ from a simplicial set $X$ to a cubical set $Q$ and the
corresponding notion of twisted Cartesian product of these sets
$X\times_{\tau }Q$ are introduced. The latter becomes a cubical
set whose chain complex coincides with the standard twisted tensor
product $C_*(X)\otimes_{\tau_*}C_*(Q)$. This construction together
with the theory of twisted tensor products for homotopy G-algebras
allows to obtain multiplicative models for fibrations.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Kadeishvili-Saneblidze/permuto
The twisted Cartesian model for the double path space fibration
Tornike Kadeishvili and Samson Saneblidze
55R05, 55P35, 55U05, 52B05, 05A18, 05A19
math.AT/0210224
A. Razmadze Mathematical Institute
Georgian Academy of Sciences
M. Aleksidze st., 1
380093 Tbilisi, Georgia
kade@rmi.acnet.ge
A. Razmadze Mathematical Institute
Georgian Academy of Sciences
M. Aleksidze st., 1
380093 Tbilisi, Georgia
sane@rmi.acnet.ge
The paper introduces the notion of a truncating twisting function
from a cubical set to a permutahedral set and the corresponding
notion of twisted Cartesian product of these sets. The latter
becomes a permutocubical set that models in particular the path
space fibration on a loop space. The chain complex of this twisted
Cartesian product in fact is a comultiplicative twisted tensor
product of cubical chains of base and permutahedral chains of
fibre. This construction is formalized as a theory of twisted
tensor products for Hirsch algebras.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Klein/susp-spectra
Moduli of Suspension Spectra
by John R. Klein
Wayne State University
klein@math.wsu.edu
For a 1-connected spectrum E, we study the moduli space of suspension
spectra which come equipped with a weak equivalence to E. We construct a
spectral sequence converging to the homotopy of the moduli space in
positive degrees. In the metastable range, we get a complete
homotopical classification of the path components of the moduli space.
Our main tool is Goodwillie's calculus of homotopy functors.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Levi-Oliver/sol
Construction of 2-local finite groups of a type studied by Solomon and Benson
by Ran Levi and Bob Oliver
A $p$-local finite group is an algebraic structure with a classifying
space which has many of the properties of $p$-completed classifying spaces
of finite groups. In this paper, we construct a family of 2-local finite
groups, which are exotic in the following sense: they are based on
certain fusion systems over the Sylow 2-subgroup of $\Spin_7(q)$ ($q$ an
odd prime power) shown by Solomon not to occur as the 2-fusion
in any actual finite group. Thus, the resulting classifying spaces are not
homotopy equivalent to the $2$-completed classifying space of any finite
group. As predicted by Benson, these classifying spaces are also very
closely related to the Dwyer-Wilkerson space $BDI(4)$.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/Rodriguez-Scherer-Viruel/notsimple3
Jose L. Rodriguez, Jerome Scherer, and Antonio Viruel
55P60, 20E32, 20D45
math.AT/0210405
Universidad de Almeria, Universitat Autonoma de Barcelona, and
Universidad de Malaga, Spain
jlrodri@ual.es, jscherer@mat.uab.es, viruel@agt.cie.uma.es
Often a localization functor (in the category of groups) sends a
finite simple group to another finite simple group. We study when
such a localization also induces a localization between the
automorphism groups and between the universal central extensions.
As a consequence we exhibit many examples of localizations of
finite simple groups which are not simple.
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