Subject: new Hopf listings Date: 02 Jan 2002 09:32:58 -0500 From: Mark Hovey To: dmd1@lehigh.edu Happy New Year! 4 new papers this time, from Bendersky-Hunton, Chorny (2), and Hunton-Schuster. Mark Hovey New papers appearing on hopf between 12/12/01 and 01/02/02 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Bendersky-Hunton/BH2 On the coalgebraic ring and Bousfield-Kan spectral sequence for a Landweber exact spectrum Martin Bendersky and John R. Hunton We construct a Bousfield-Kan (unstable Adams) spectral sequence based on an arbitrary (and not necessarily connective) ring spectrum $E$ with unit and which is related to the homotopy groups of a certain unstable $E$ completion $\xe$ of a space $X$. For $E$ an S-Algebra this completion agrees with that of the first author and R. Thompson. We also establish in detail the Hopf algebra structure of the unstable cooperations (the coalgebraic module) $E_*(\EE_*)$ for an arbitrary Landweber exact spectrum $E$, extending work of the second author and M. Hopkins\cite and giving basis-free descriptions of the modules of primitives and indecomposables. Taken together, these results enable us to give a simple description of the $E_2$-term of the $E$-theory Bousfield-Kan spectral sequence when $E$ is any Landweber exact ring spectrum with unit. This extends work of the first author and others and gives a tractable unstable Adams spectral sequence based on a $v_n$-periodic theory for all~$n$. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/ChornyB/diag An example of a non-cofibrantly generated model category Boris Chorny AMS Classification numbers Primary 55U35; Secondary 55P91, 18G55 Centre de Recerca Matematica, Apartat 50, E-08193 Bellaterra (Barcelona), Spain cboris@crm.es We show that the model category of diagrams of spaces generated by a proper class of orbits is not cofibrantly generated. In particular the category of maps between spaces may be given a non-cofibrantly generated model structure. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/ChornyB/ehomology Equivariant cellular homology and its applications Boris Chorny AMS Classification numbers Primary 55N91; Secondary 55P91, 57S99 Einstein Institute of Mathematics, Edmond Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem 91904, Israel chorny@math.huji.ac.il In this work we develop a cellular equivariant homology functor and apply it to prove an equivariant Euler-Poincare formula and an equivariant Lefschetz theorem. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Hunton-Schuster/subalg Title: Subalgebras of group cohomology defined by infinite loop spaces Authors: John R. Hunton Bj"orn Schuster MSC: 20J06 55N20 55P47 (primary), 55R40 19A22 55P60 (secondary) arXiv: math.AT/0112169 Addresses: The Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, England Department of Mathematics, University of Wuppertal, Gaussstr.~20, D-42097 Wuppertal, Germany. Abstract: We study natural subalgebras Ch_E(G) of group cohomology defined in terms of infinite loop spaces E and give representation theoretic descriptions of those based on QS^0 and the Johnson-Wilson theories E(n). We describe the subalgebras arising from the Brown-Peterson spectra BP and as a result give a simple reproof of Yagita's theorem that the image of BP^*(BG) in H^*(BG;F_p) is F-isomorphic to the whole cohomology ring; the same result is shown to hold with BP replaced by any complex oriented theory E with a map of ring spectra from E to HF_p which is non-trivial in homotopy. We also extend the constructions to define subalgebras of H^*(X;F_p) for any space X; when X is finite we show that the subalgebras Ch_{E(n)}(X) give a natural unstable chromatic filtration of H^*(X;F_p). ---------------------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://www.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 WWW client (Netscape or Internet Explorer) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to Purdue seminars, and other math related things on this page as well. The largest archive of math preprints is at http://xxx.lanl.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 xxx, send e-mail to math@xxx.lanl.gov with subject line "subscribe" (without quotes), and with the body of the message "add AT" (without quotes). You can also access Hopf through ftp. Ftp to hopf.math.purdue.edu, and login as ftp. Then cd to pub. Files are organized by author name, so papers by me are in pub/Hovey. If you want to download a file using ftp, you must type binary before you type get . To put a paper of yours on the archive, cd to /pub/incoming. Transfer the dvi file using binary, by first typing binary then put You should also transfer 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@math.purdue.edu telling him what you have uploaded. I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive.