Subject: new Hopf listings From: Mark Hovey Date: 04 Nov 2004 05:49:34 -0500 To: dmd1@lehigh.edu 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)}S0 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 $E2$ term of the GAHSS in the case of 2--exact functors on Moore spaces. ---------------------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.