6 new papers this month, from Boardman-Wilson,
Goerss-Henn-Mahowald-Rezk, Lewis-Mandell, McClure, Turiel, and Wodarz.  

                  Mark Hovey

New papers appearing on hopf between 10/15/04 and 11/04/04

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Boardman-Wilson/BWonPn

Title: k(n)-torsion-free H-spaces and P(n)-cohomology
Authors: J. Michael Boardman, W. Stephen Wilson
E-mail: boardman@math.jhu.edu, wsw@math.jhu.edu
Address: Dept. of Mathematics, Johns Hopkins University,
	3400 N. Charles St., Baltimore MD 21218-2686
AMS Classifications: Primary 55N22, 55P45

Abstract: In his thesis, the second author split the H-space that
represents Brown-Peterson cohomology BP^k(-) into indecomposable factors,
which have torsion-free homotopy and homology.  Here, we do the same for
the related spectrum P(n), by constructing idempotent operations in
P(n)-cohomology P(n)^k(-) in the style of Boardman-Johnson-Wilson; this
relies heavily on the Ravenel-Wilson determination of the relevant Hopf
ring.  The resulting (i-1)-connected H-spaces Y_i have free connective
Morava K-homology k(n)_*(Y_i), and may be built from the spaces in the
Omega-spectrum for k(n) using only v_n-torsion invariants.

We also extend Quillen's theorem on complex cobordism to show that for any
space X, the P(n)_*-module P(n)^*(X) is generated by elements of P(n)^i(X)
for i>=0.  This result is essential for the work of Ravenel-Wilson-Yagita,
which in many cases allows one to compute BP-cohomology from Morava K-theory.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Goerss-Henn-Mahowald-Rezk/ghmr

Title: A resolution of the K(2)-local sphere at the prime 3

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

Northwestern University, Universit\'e Louis Pasteur et CNRS, 
Northwestern University, University of Illinois Urbana, IL 61801

(This is an updated version)

ABSTRACT We develop a framework for displaying
the stable homotopy theory of the sphere, at least after localization 
at the second Morava K-theory K(2). At the
prime 3, we write the spectrum L_{K(2)}S^0 as the inverse
limit of a tower of fibrations with four layers. The successive fibers are
of the form E_2^{hF} where F is a finite subgroup of the Morava
stabilizer group and E_2 is the second Morava or Lubin-Tate
homology theory. We give explicit calculation of the homotopy groups
of these fibers. The case n=2 at p=3 represents the edge
of our current knowledge: n=1 is classical and at n=2, the prime 3
is the largest prime where the Morava stabilizer group has a p-torsion
subgroup, so that the homotopy theory is not entirely algebraic.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Lewis-Mandell/Lewis-Mandell-UCT

Equivariant Universal Coefficient and Kunneth Spectral Sequences

L. Gaunce Lewis, Jr.
Department of Mathematics
Syracuse University
Syracuse, NY 13244-1150
lglewis@syr.edu

Michael A. Mandell
DPMMS, University of Cambridge
Wilberforce Road
Cambridge CB3 0WB
UK
M.A.Mandell@dpmms.cam.ac.uk

AMS Classification: Primary 55N91; Secondary 55P43,55U20,55U25}

Abstract
We construct hyper-homology spectral sequences of Z-graded and
ROG-graded Mackey functors for Ext and Tor over G-equivariant
S-algebras (A-infty ring spectra) for finite groups G.  These
specialize to universal coefficient and Kunneth spectral sequences.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/McClure/intersection

On the chain-level intersection pairing for PL manifolds.

J.E. McClure
mcclure@math.purdue.edu
AMS classification numbers: 57Q65; 18D50
Posted on arXiv: math.QA/0410450

Abstract: Let M be a compact oriented PL manifold and let C_*M be its PL 
chain complex.  The domain of the chain-level intersection pairing is a 
subcomplex G of C_*M\otimes C_*M.  We prove that G is a ``full'' 
subcomplex, that is, the inclusion of G in C_*M \otimes C_*M is a 
quasi-isomorphism.  An analogous result is true for the domain of the 
iterated intersection pairing.  Using this, we show that the intersection 
pairing gives C_*M a structure of partially defined commutative DGA, which 
in particular implies that C_*M is canonically quasi-isomorphic to an 
E_\infty chain algebra.

5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Turiel/poly

Polynomial Maps and Even Dimensional Spheres

Javier Turiel
turiel@agt.cie.uma.es

Abstract: We construct, for every even dimensional sphere $S^n$,
$n >1$, and every odd integer $k$, a homogeneous polynomial map
$f: S^{n}\to S^{n}$ of Brouwer degree $k$ and algebraic degree
$2|k|-1$.

6.
http://hopf.math.purdue.edu/cgi-bin/generate?/Wodarz/ExactHomotopyFunctors

Title: Exactness of Homotopy Functors of Spaces

Author: Nathan Wodarz
AMS Classification: 55P65, 55T25
Address: Grand Valley State University, Allendale, MI
E-mail: wodarzn@gvsu.edu
 
Abstract: We will provide an analysis of the generalized
Atiyah--Hirzebruch spectral sequence (GAHSS), which was introduced by
Hakim-Hashemi and Kahn. To do so, we introduce a new class of functors,
called $n$--exact functors, which are analogous to Goodwillie's
$n$--excisive functors. In the study of these functors, we introduce a
new spectral sequence, the homological Barratt--Goerss spectral sequence
(HBGSS), which has properties similar to those of the classical
Barratt--Goerss Spectral Sequence on homotopy. We close by giving an
identification of the $E^2$ term of the GAHSS in the case of 2--exact
functors on Moore spaces.


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