Subject:
new Hopf listings
From:
Mark Hovey
Date:
14 Dec 2004 11:16:24 -0500
To:
dmd1@lehigh.edu
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 CaP2 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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