---------------------------------
Happy New Year!  This is the beginning of the 10th year I have been
doing this.  

10 new papers this time, from Bubenik, ChornyB (2), Gillespie, Hovey,
Jardine, Lueck, Mitchell, Pengelley-Williams, and Vavpatic-Viruel.  

                  Mark Hovey

New papers appearing on hopf between 11/25/03 and 1/05/04

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bubenik/fsi

Title: Free and semi-inert cell attachments
Author: Peter Bubenik
Author's e-mail address: peter.bubenik@epfl.ch
AMS classification number: 55P35 (Primary) 16E45 (Secondary)
arXive submission number: math.AT/0312387

Abstract:
Let $Y$ be the space obtained by attaching a finite-type wedge of cells
to a simply-connected, finite-type CW-complex.

We introduce the free and semi-inert conditions on the attaching map
which broadly generalize the previously studied inert condition.  Under
these conditions we determine $H_*(\Omega Y;R)$ as an $R$-module and as
an $R$-algebra respectively.  Under a further condition we show that
$H_*(\Omega Y;R)$ is generated by Hurewicz images.

As an example we study an infinite family of spaces constructed using
only semi-inert cell attachments.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/ChornyB/Localization1

Title: Localization with respect to a class of maps I - Equivariant
localization of diagrams of spaces 
Author: Boris Chorny
Author's e-mail address: bchorny2@uwo.ca

Abstract:
Homotopical localizations with respect to a set of maps are known to
exist in cofibrantly generated model categories (satisfying additional
assumptions). In this paper we expand the existing framework, so that it
will apply to not necessarily cofibrantly generated model categories
and, more important, will allow for a localization with respect to a
class of maps (satisfying some restrictive conditions).

We illustrate our technique by applying it to the equivariant model
category of diagrams of spaces. This model category is not cofibrantly
generated. We give conditions on a class of maps which ensure the
existence of the localization functor; these conditions are satisfied by
any set of maps and by the classes of maps which induce ordinary
localizations on the generalized fixed-points sets.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/ChornyB/Localization2

Title: Localization with respect to a class of maps II - Equivariant
cellularization and its application
Author: Boris Chorny
Author's e-mail address: bchorny2@uwo.ca

Abstract: We present an example of a homotopical localization functor
which is not a localization with respect to any set of maps. Our example
arises from equivariant homotopy theory. The technique of equivariant
cellularization is developed and applied to the proof of the main
result.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Gillespie/sheafproblem

Title: The flat model structure on Ch(O)
Author: James Gillespie
Email: jrg21@psu.edu

Abstract: Let Ch(O) be the category of chain complexes of O-modules on a
topological space T (where O is a sheaf of rings on T ). We put a
Quillen model structure on this category in which the cofibrant objects
are built out of flat modules. More precisely, these are the dg-flat
complexes. Dually, the fibrant objects will be called dg-cotorsion
complexes. We show that this model structure is monoidal, solving the
previous problem of not having any monoidal model structure on Ch(O). As
a corollary, we have a general framework for doing homological algebra
in the category O-MOD of O-modules. I.e., we have a natural way to
define the functors Ext and Tor in O-MOD.

5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Hovey/morava-E-operations

Operations and co-operations in Morava $E$-theory

Mark Hovey

Wesleyan University 
mhovey@wesleyan.edu 

In this paper, we revisit the calculations of the operations and
co-operations in Morava E-theory.  Recall that the co-operations are the
continuous functions from a profinite group G that is a version of the
Morava stabilizer group to E_*.  The operations are the completed
twisted group ring E_*[[G]].  

These results have appeared in the literature before.  The advantage of
this paper is that it is self-contained, works out all the details that
are usually skipped over, and uses a new approach, not directly
dependent on Morava's Annals paper on comodules, that the author finds
fairly simple and elegant.  Most of all, though, the author wrote this
paper because he was unable to understand the proofs in the
literature. He hopes it will be useful for people in the same unhappy
situation.  

6.
http://hopf.math.purdue.edu/cgi-bin/generate?/Jardine/cat5

Categorical homotopy theory
J.F. Jardine

This paper is an exposition and extension of the ideas and
methods of Cisinksi, set at the level of A-presheaves on a small
Grothendieck site, where A is an arbitrary test category in the sense of
Grothendieck. The model structures for the category of simplicial
presheaves and all of its localizations can be modelled by A-presheaves
in the sense that there is a corresponding model structure for
A-presheaves with an equivalent homotopy category. The theory
specializes, for example, to the homotopy theories of cubical sets,
cubical presheaves, and gives a cubical model for motivic homotopy
theory. The applications of Cisinski's ideas are explained in some
detail for cubical sets.

7.
http://hopf.math.purdue.edu/cgi-bin/generate?/Lueck/lueck_classifyingspaces1203

Title:  Survey on Classifying Spaces for Families of Subgroups
Author: Wolfgang Lueck

AMS Classification numbers: 55R35, 57S99, 20F65, 18G99

Address: Mathematisches Institut der
         Westfaelischen Wilhelms Universitaet
         Einsteinstr. 62
         48149 Muenster
         Germany

Abstract: 
We define for a topological group G and a family of subgroups F two
versions for the classifying space for the family F, the G-CW-version
E_F(G) and the numerable G-space version J_F(G). They agree if G is
discrete, or if G is a Lie group and each element in F compact, or if G
is totally disconnected and F is the family of compact subgroups or of
compact open subgroups. We discuss special geometric models for these
spaces for the family of compact open groups in special cases such as
almost connected groups G and word hyperbolic groups G. We deal with the
question whether there are finite models, models of finite type, finite
dimensional models. We also discuss the relevance of these spaces for
the Baum-Connes Conjecture about the topological K-theory of the reduced
group C^*-algebra, for the Farrell-Jones Conjecture about the algebraic
K- and L-theory of group rings, for Completion Theorems and for
classifying spaces for equivariant vector bundles and for other
situations.
 
8.
http://hopf.math.purdue.edu/cgi-bin/generate?/Mitchell/sw

Author: Stephen A. Mitchell
Title: Stiefel-Whitney classes, united K-theory and real embeddings of
number rings
e-mail: mitchell@math.washington.edu

We study the relations among the Stiefel-Whitney classes associated to
the real embeddings of a number ring. Our results depend on a
computation of the real and self-conjugate K-theory of the algebraic
K-theory spectrum of the number ring. 

9.
http://hopf.math.purdue.edu/cgi-bin/generate?/Pengelley-Williams/subsmalg

			Global Structure of the
 	mod 2 Symmetric Algebra over the Steenrod algebra.

		David J. Pengelley (davidp@nmsu.edu)
		  Frank Williams (frank@nmsu.edu)


 The algebra S of symmetric invariants over the field with two elements
is an unstable algebra over the Steenrod algebra A and is isomorphic
to the mod two cohomology of BO, the classifying space for vector 
bundles.  We provide a minimal presentation for S in the category of
unstable A-algebras, i.e., a minimal set of generators and a minimal
set of relations.
 From this we produce minimal presentations for various unstable
A-algebras associated with the cohomology of related spaces, such as 
the BO(2^n - 1) that classify finite dimensional vector bundles, and
the connected covers of BO.  The presentations then show that certain
of these unstable A-algebras coalesce to produce the mod 2 Dickson
algebras, and we speculate about possible related topological 
realizability.
 Our methods also produce a related simple A-module presentation of the
cohomology of infinite-dimensional real projective space, with a
filtration having well-known filtered quotients.

10.
http://hopf.math.purdue.edu/cgi-bin/generate?/Vavpetic-Viruel/PU

On the mod p cohomology of BPU(p)

Ales Vavpetic
Fakulteta za matematiko in fiziko
Univerza v Ljubljani
Jadranska 19
SI-1111 Ljubljana
Slovenia
ales.vavpetic@fmf.uni-lj.si

Antonio Viruel
Dpto de Algebra, Geometria y Topologia
Universidad de Malaga
Apdo correos 59
E29080 Malaga
Spain
viruel@agt.cie.uma.es

AMS Classification numbers: 55R35, 55P15

ABSTRACT: We study the mod p cohomology of the classifying space of the
projective unitary group PU(p). We first proof that old conjectures due
to J.F. Adams, and Kono and Yagita about the structure of the mod p
cohomology of classifying space of connected compact Lie groups held in
the case of PU(p). Finally, we proof that the classifying space of the
projective unitary group PU(p) is determined by its mod p cohomology as
an unstable algebra over the Steenrod algebra for p>3, completing
previous works of Dwyer, Miller, Wilkerson at prime 2 and Broto, Viruel
at prime 3.


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