There are 4 new papers this time, from Biedermann-Chorny-Roendigs,
Bubenik-Worytkiewicz, DavisD-Theriault, and Fresse. 
                  Mark Hovey

New papers appearing on hopf between 1/4/06 and 2/8/06

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Biedermann-Chorny-Roendigs/biedermann-chorny-roendigs

 Title: Goodwillie's calculus and model categories

  Author(s): Georg Biedermann, Boris Chorny, Oliver Roendigs

 Abstract: 
The category of small covariant functors from simplicial sets to
simplicial sets supports the projective model structure. In this paper
we construct various localizations of the projective model structure and
also give a variant for functors from simplicial sets to spectra. We
apply these model categories in the study of calculus of functors,
namely for classification of polynomial and homogeneous
functors. Finally we show that the $n$-th derivative induces a Quillen
map between the $n$-homogeneous model structure on small functors from
pointed simplicial sets to spectra and the category of spectra with
$\Sigma_n$-action. We consider also a finitary version of the
$n$-homogeneous model structure and the $n$-homogeneous model structure
on functors from pointed finite simplicial sets to spectra. In these two
cases the above Quillen map becomes a Quillen equivalence. This improves
the classification of finitary homogeneous functors by T. G. Goodwillie.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bubenik-Worytkiewicz/lps

title: A model category for local po-spaces

author: Peter Bubenik
author: Krzysztof Worytkiewicz


to appear in: Homology, Homotopy and Applications

abstract:
Locally partial-ordered spaces (local po-spaces) have been used to model
concurrent systems. We provide equivalences for these spaces by
constructing a model category containing the category of local
po-spaces. We show the category of simplicial presheaves on local
po-spaces can be given Jardine's model structure, in which we identify
the weak equivalences between local po-spaces. In the process we give an
equivalence between the category of sheaves on a local po-space and the
category of {\'e}tale bundles over a local po-space. Finally we describe
a localization that should provide a good framework for studying
concurrent systems.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/DavisD-Theriault/theri6

Odd-primary homotopy exponents of compact simple Lie groups

Donald M. Davis and Stephen D. Theriault

We note that a recent result of the second author yields
upper bounds for odd-primary homotopy exponents of compact
simple Lie groups which are often quite close to the lower
bounds obtained from v1-periodic homotopy theory.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Fresse/Bar-StructureUniqueness

Title: The bar construction of an $E$-infinity algebra
Author: Benoit Fresse


Abstract: We consider the classical reduced bar construction of
associative algebras B(A). If the product of A is commutative, then B(A)
can be equipped with the classical shuffle product, so that B(A) is
still a commutative algebra.  This assertion can be generalized for
algebras which are commutative up to homotopy.  Namely, one observes
that the bar construction of an E-infinite algebra B(A) can be endowed
with the structure of an E-infinite algebra.

The purpose of this article is to give an existence and uniqueness
theorem for this claim.  We would like to insist on the uniqueness
property: our statement makes the construction of $E$-infinite
structures easier and more flexible.  Therefore, the proof of our
existence theorem differs from other constructions of the literature.
In addition, the uniqueness property allows to give easily a homotopy
interpretation of the bar construction.

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