7 papers this by time, from Ghienne, Goerss-Henn-Mahowald,
Ishiguro-LeeHS, McAuley, Panov-Ray-Vogt, Pengelley-Williams, and Sinha.

Mark Hovey

New papers appearing on hopf between 03/05/02 and 04/03/02

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Ghienne/ghiennephsnt

Title of paper:      Phantom maps, SNT-theory, and natural filtrations
		     on lim^1 sets. 
Author:              Pierre GHIENNE.
AMS Classification:  55Q05, 55S37, 55P15.
Adress of author:    Matematisk Institut, Universitetsparken 5, DK--2100
		     København. 
E-mail adress:       ghienne@math.ku.dk
Text of abstract:

 We study the so-called Gray filtration on the set of phantom maps
between two spaces. Using both its algebraic characterization and the
Sullivan completion approach to phantom maps, we generalize some of the
recent results of Le, McGibbon and Strom. We particularly emphasize on
the set of phantom maps with infinite Gray index, describing it in an
original algebraic way.

We furthermore introduce and study a natural filtration on
SNT-sets (that is sets of homotopy types of spaces having the same
$n$-type for all $n$), which appears to have the same algebraic
characterization of the Gray one on phantom maps. For spaces whose
rational homotopy type is that of an $H$-space or a co-$H$-space, we
establish criteria permitting to determinate those subsets of this
filtration which are non trivial, generalizing work of McGibbon and M\o
ller.
	 
We finally describe algebraically the natural connection between
phantom maps and SNT-theory, associating to a phantom map its homotopy
fiber or cofiber. We use this description to show that this connection
respect filtrations, and to find generic examples of spaces for which
the filtration on the corresponding SNT-set consists of infinitely many
strict inclusions.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Goerss-Henn-Mahowald/18-02-ghm

Title: The homotopy of L_2V(1) for the prime 3

Authors:  Paul Goerss, Hans-Werner Henn and Mark Mahowald

Adresses: 
Northwestern University, Universite Louis Pasteur, Northwestern University

ABSTRACT 

Let V(1) be the Toda-Smith complex for the prime 3.  We give a complete
calculation of the homotopy groups of the L_2-localization of V(1) by
making use of the higher real K-theory EO_2 of Hopkins and Miller and
related homotopy fixed point spectra.  In particular we resolve an
ambiguity which was left in an earlier approach of Shimomura whose
computation was almost complete but left an unspecified parameter still
to be determined.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Ishiguro-LeeHS/2_21_02

Homotopy fixed point sets and actions on homogeneous spaces of
$p$--compact groups  

Kenshi Ishiguro  (kenshi@cis.fukuoka-u.ac.jp)
Fukuoka University,  Fukuoka  814-0180, Japan

and

Hyang-Sook Lee  (hsl@mm.ewha.ac.kr)
Ewha Womans University,  Seoul, Korea

We generalize a result of Dror Farjoun and Zabrodsky on the relationship
between fixed point sets and homotopy fixed point sets, which is related
to the generalized Sullivan Conjecture.  As an application, we discuss
extension problems considering actions on homogeneous spaces of
$p$--compact groups.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/McAuley/mcauleypaper

This is another new version of Louis McAuley's paper titled "A proof of
the Hilbert-Smith conjecture".

5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Panov-Ray-Vogt/0202081

Title: Colimits, Stanley-Reisner algebras, and loop spaces

Authors: Taras Panov, Nigel Ray, and Rainer Vogt

Addresses:
Department of Mathematics and Mechanics, Moscow State
University, 119899 Moscow, Russia;
Department of Mathematics, University of Manchester,
Manchester M13 9PL, England;
Fachbereich Mathematik/Informatik, Universitaet Osnabrueck,
D-49069 Osnabrueck, Germany.

E-mail addresses:
tpanov@mech.math.msu.su
nige@ma.man.ac.uk
rainer@mathematik.uni-osnabrueck.de

Arxiv: math.AT/0202081

Abstract:
We study diagrams associated with a finite simplicial complex K, in
various algebraic and topological categories. We relate their colimits
to familiar structures in algebra, combinatorics, geometry and
topology. These include: right-angled Artin and Coxeter groups (and
their complex analogues, which we call circulation groups);
Stanley-Reisner algebras and coalgebras; Davis and Januszkiewicz's
spaces DJ(K) associated with toric manifolds and their generalisations;
and coordinate subspace arrangements. When K is a flag complex, we
extend well-known results on Artin and Coxeter groups by confirming that
the relevant circulation group is homotopy equivalent to the space of
loops $\Omega DJ(K)$. We define homotopy colimits for diagrams of
topological monoids and topological groups, and show they commute with
the formation of classifying spaces in a suitably generalised sense. We
deduce that the homotopy colimit of the appropriate diagram of
topological groups is a model for $\Omega DJ(K)$ for an arbitrary
complex K, and that the natural projection onto the original colimit is
a homotopy equivalence when K is flag. In this case, the two models are
compatible.

6.
http://hopf.math.purdue.edu/cgi-bin/generate?/Pengelley-Williams/toclarence

The global structure of odd-primary Dickson algebras as algebras over
the Steenrod algebra

David J. Pengelley
New Mexico State University
Las Cruces, NM 88003
davidp@nmsu.edu
Frank Williams
New Mexico State University
Las Cruces, NM 88003
frank@nmsu.edu

Primary 55S05; Secondary 13A50, 16W30, 16W22, 16W50, 55S10

We prove a conjecture made by Frank Peterson on the global structure of
the Dickson algebras arising as odd primary general linear group
invariants. The Dickson algebra $W_{n}$ of invariants in a rank $n$
polynomial algebra over $% \mathbb{F}_{p}$ is an unstable algebra over
the mod $p$ Steenrod algebra. We prove that $W_{n}$ is a free unstable
algebra on a certain cyclic module, modulo just one additional
relation. The result is both similar to and different from the
corresponding result we previously obtained with Frank Peterson at the
prime $2$. We also extend our characterization to the algebras of
invariants under the special linear groups.

7.
http://hopf.math.purdue.edu/cgi-bin/generate?/Sinha/knots

Title: The topology of spaces of knots.
Author: Dev P. Sinha 
AMS Class: 57R40 (primary); 55T35, 57Q45 (secondary).
LANL ID: math.AT/0202287
Addresses: Department of Mathematics, University of Oregon, Eugene OR and
Department of Mathematics, Brown University, Providence RI 
Email: dps@math.brown.edu
Included EPS files: smallpenta.eps, smalltreepenta.eps

Abstract:
We present two models for the space of knots which have endpoints at
fixed boundary points in a manifold with boundary, one model defined as
an inverse limit of mapping spaces and another which is cosimplicial.
These models are homotopy equivalent to the corresponding knot spaces
when the dimension of the ambient manifold is greater than three, and
there are spectral sequences with identifiable $E^1$ terms which
converge to their cohomology and homotopy groups.  The combinatorics of
the spectral sequences is comparable to combinatorics which arises in
finite-type invariant theory.