Happy New Year!  4 new papers this time, from Bendersky-Hunton, Chorny
(2), and Hunton-Schuster.

Mark Hovey

New papers appearing on hopf between 12/12/01 and 01/02/02

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bendersky-Hunton/BH2

On the coalgebraic ring and Bousfield-Kan spectral sequence
for a Landweber exact spectrum

Martin Bendersky and John R. Hunton

We construct a Bousfield-Kan (unstable Adams) spectral sequence
based on an arbitrary (and not necessarily connective) ring
spectrum $E$ with unit and which is related to the homotopy groups
of a certain unstable $E$ completion $\xe$ of a space $X$. For $E$
an S-Algebra this completion agrees with that of the first author
and R. Thompson. We also  establish in detail the Hopf algebra
structure of the unstable cooperations (the coalgebraic module)
$E_*(\EE_*)$ for an arbitrary Landweber exact spectrum $E$,
extending work of the second author and M. Hopkins\cite and giving
basis-free descriptions of the modules of primitives and
indecomposables. Taken together, these results enable us to give a
simple description of the $E_2$-term of the $E$-theory
Bousfield-Kan spectral sequence when $E$ is any Landweber exact
ring spectrum with unit. This extends work of the first author and
others and gives a tractable unstable Adams spectral sequence
based on a $v_n$-periodic theory for all~$n$.

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

An example of a non-cofibrantly generated model category

Boris Chorny

AMS Classification numbers
Primary 55U35; Secondary 55P91, 18G55

Centre de Recerca Matematica, Apartat 50, E-08193 Bellaterra
(Barcelona), Spain 
cboris@crm.es

We show that the model category of diagrams of spaces generated by a
proper class of orbits is not cofibrantly generated. In particular the
category of maps between spaces may be given a non-cofibrantly generated
model structure.

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

Equivariant cellular homology and its applications

Boris Chorny

AMS Classification numbers
Primary 55N91; Secondary 55P91, 57S99

Einstein Institute of Mathematics, Edmond Safra Campus,
Givat Ram, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
chorny@math.huji.ac.il

In this work we develop a cellular equivariant homology
functor and apply it to prove an equivariant Euler-Poincare formula and
an equivariant Lefschetz theorem.


4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Hunton-Schuster/subalg

Title:     Subalgebras of group cohomology defined by infinite loop spaces
Authors:   John R. Hunton <J.Hunton@mcs.le.ac.uk>
           Bj"orn Schuster <schuster@math.uni-wuppertal.de>
MSC:       20J06 55N20 55P47 (primary), 55R40 19A22 55P60 (secondary)
arXiv:     math.AT/0112169
Addresses: The Department of Mathematics and Computer Science, University of 
	   Leicester, University Road, Leicester, LE1 7RH, England
	   Department of Mathematics, University of Wuppertal, Gaussstr.~20, 
	   D-42097 Wuppertal, Germany.

Abstract:
We study natural subalgebras Ch_E(G) of group cohomology defined in terms
of infinite loop spaces E and give representation theoretic descriptions of
those based on QS^0 and the Johnson-Wilson theories E(n). We describe the
subalgebras arising from the Brown-Peterson spectra BP and as a result give
a simple reproof of Yagita's theorem that the image of BP^*(BG) in
H^*(BG;F_p) is F-isomorphic to the whole cohomology ring; the same result
is shown to hold with BP replaced by any complex oriented theory E with a
map of ring spectra from E to HF_p which is non-trivial in homotopy. We
also extend the constructions to define subalgebras of H^*(X;F_p) for any
space X; when X is finite we show that the subalgebras Ch_{E(n)}(X)
give a natural unstable chromatic filtration of H^*(X;F_p).