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Sorry for the delay this month.  The semester is finally over!

6 new papers this month, from Angeltveit, Bokstedt-Ottosen (2),
Castellana-Crespo-Scherer, Kitchloo-Wilson, and May.  

                  Mark Hovey

New papers appearing on hopf between 11/04/04 and 12/14/04

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Angeltveit/Ainfinity

Title: $A_\infty$ obstruction theory and the strict associativity of $E/I$

Author: Vigleik Angeltveit

E-mail address: vigleik@math.mit.edu

Address: Department of Mathematics, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139, USA

Abstract: We prove that for a ring spectrum $K$ with a perfect universal 
coefficient formula, the obstructions to extending the multiplication 
to an $A_\infty$ multiplication lie in $Ext^{*,*}_{K_*K^{op}}(K_*,K_*)$.
As a corollary, we show that if $E$ is even and $I=(x_1,x_2,\ldots)$ is
a regular sequence in $E_*$, then any product on $E/I$ can be extended
to an $A_\infty$ multiplication.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bokstedt-Ottosen/hiem

Ttile: An alternative approach to homotopy operations

Authors: Marcel Bokstedt and Iver Ottosen

Email: marcel@imf.au.dk, ottosen@imf.au.dk

Address: 
Department of Mathematical Sciences, 
University of Aarhus,
Ny Munkegade, Building 530, 
DK-8000 Aarhus C, Denmark

Abstract: We give a particular choice of the higher Eilenberg-MacLane
maps of a simplicial ring by a recursive formula.  This choice leads to
a simple description of the homotopy operations for simplicial
Z/2-algebras.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bokstedt-Ottosen/kkp

Title: A splitting result for the free loop space of 
spheres and projective spaces

Authors: Marcel Bokstedt and Iver Ottosen

Email: marcel@imf.au.dk, ottosen@imf.au.dk

Address: 
Department of Mathematical Sciences, 
University of Aarhus,
Ny Munkegade, Building 530, 
DK-8000 Aarhus C, Denmark

MSC: 55P35, 18G50, 55S10

Abstract: Let X be a 1-connected compact space such that 
the algebra H*(X;Z/2) is generated by one single element. 
We compute the cohomology of the free loop space H*(LX;Z/2) 
including the Steenrod algebra action. When X is a projective 
space CP^n, HP^n, the Cayley projective plane CaP^2 or a 
sphere S^m we obtain a splitting result for integral and 
mod two cohomology of the suspension spectrum of LX_+. The 
splitting is in terms of the suspension spectrum of X_+ and 
the Thom spaces of the q-fold Whitney sums of the tangent 
bundle over X for non negative integers q.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Castellana-Crespo-Scherer/CWPostH

Title: Postnikov pieces and BZ/p-homotopy theory

Authors: Natalia Castellana, Juan A. Crespo, Jerome Scherer

email: natalia@mat.uab.es, JuanAlfonso.Crespo@uab.es,
jscherer@mat.uab.es

AMS classification number: 55R35; 55P60, 55P20, 20F18

ArXiv submission number: math.AT/0409399

Abstract: We present a constructive method to compute the
cellularization with respect to K(Z/p, m) for any integer m > 0 of
a large class of H-spaces, namely all those which have a finite
number of non-trivial K(Z/p, m)-homotopy groups (the pointed
mapping space map( K(Z/p, m), X) is a Postnikov piece). We prove
in particular that the K(Z/p, m)-cellularization of an H-space
having a finite number of K(Z/p, m)-homotopy groups is a p-torsion
Postnikov piece. Along the way we characterize the BZ/p^r-cellular
classifying spaces of nilpotent groups.

5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Kitchloo-Wilson/kitchloo-wilson-ER2

Title:
On the Hopf ring for ${ER(n)}$

Authors:
Nitu Kitchloo
Department of Mathematics 
University of California, 
San Diego (UCSD) 
La Jolla, CA 92093-0112 
nitu@math.ucsd.edu

W. Stephen Wilson
Department of Mathematics 
Johns Hopkins University 
Baltimore, Maryland 21218 
wsw@math.jhu.edu

Kriz and Hu construct a real Johnson-Wilson spectrum, $ER(n)$,
which is $2^{n+2}(2^n-1)$ periodic.  $ER(1)$ is just $KO_{(2)}$.  
We do two things in this paper.  First, we compute the homology 
of the $2^{n+2}k}$ spaces in the Omega spectrum for $ER(n)$.
There are $2^n-1$ of them and their double is the Hopf ring
for $E(n)$.  As a byproduct of this we get the homology of the 
zeroth spaces for the Omega spectrum for real complex cobordism 
and real Brown-Peterson cohomology.  The second result is to 
compute the homology Hopf ring for all 48 spaces in the Omega 
spectrum for $ER(2)$.  This turns out to be generated by very 
few elements.

6.
http://hopf.math.purdue.edu/cgi-bin/generate?/May/Split

A note on the splitting principle
J.P. May
may@math.uchicago.edu
55R40, 55N99

We offer a new* perspective on the splitting principle.
We give an easy proof that applies to all classical 
types of vector bundles and in fact to $G$-bundles for 
any compact connected Lie group $G$. The perspective
gives precise calculational information and directly 
ties the splitting principle to the specification of 
characteristic classes in terms of classifying spaces.

* Note to the list: if this is not new, please let me 
know --- it shouldn't be, but it was to those experts 
I tried it out on.

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