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. ---------------------Instructions----------------------------- To subscribe or unsubscribe to this list, send a message to Don Davis at dmd1@lehigh.edu with your e-mail address and name. Please make sure he is using the correct e-mail address for you. To see past issues of this mailing list, point your WWW browser to http://math.wesleyan.edu/~mhovey/archive/ If this doesn't work or is missing a few issues, try http://www.lehigh.edu/~dmd1/algtop.html which also has the other messages sent to Don's list. To get the papers listed above, point your Web browser to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There is a web form for submitting papers to Hopf on this site as well. You should submit an abstract as well. Clarence has explicit instructions for the form of this abstract: see http://hopf.math.purdue.edu/new-html/submissions.html In particular, your abstract is meant to be read by humans, so should be as readable as possible. I reserve the right to edit unreadable abstracts. You should then e-mail Clarence at wilker at math.purdue.edu telling him what you have uploaded. The largest archive of math preprints is at http://arxiv.gov There is an algebraic topology section in this archive. The most useful way to browse it or submit papers to it is via the front end developed by Greg Kuperberg: http://front.math.ucdavis.edu To get the announcements of new papers in the algebraic topology section at the arXiv, send e-mail to math@arxiv.org with subject line "subscribe" (without quotes), and with the body of the message "add AT" (without quotes). I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive.