Subject: new Hopf listings From: Mark Hovey Date: 05 Jun 2000 03:49:01 -0400 9 new papers this time, including the Mahowald-Ravenel-Shick paper returning the telescope conjecture to the community. Mark Hovey New papers uploaded to hopf between 4/9/00 and 6/4/00. 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Adem-Carlson-Karagueuzian-Milg ram/hs The Cohomology of the Sylow 2-Subgroup of the Higman-Sims Group A. Adem Mathematics Department University of Wisconsin Madison WI 53706 J. F. Carlson Mathematics Department University of Georgia Athens GA 30602 D. B. Karagueuzian Mathematics Department University of Wisconsin Madison WI 53706 R. James Milgram Mathematics Department Stanford University Stanford CA 94305 Abstract In this paper we compute the mod 2 cohomology of the Sylow 2-subgroup of the Higman--Sims group HS, one of the 26 sporadic simple groups. We obtain its Poincare series as well as an explicit description of it as a ring with 17 generators and 79 relations. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Adem-Pakianathan/adpak On the Cohomology of Central Frattini Extensions Alejandro Adem and Jonathan Pakianathan Mathematics Department University of Wisconsin Madison, Wisconsin, 53706 adem@math.wisc.edu, pakianat@math.wisc.edu Abstract In this paper we provide calculations for the mod p cohomology of certain p-groups, using topological methods. More precisely, we look at p-groups G defined as central extensions 1-> V -> G ->W ->1 of elementary abelian groups such that the mod p reduction of G/[G,G] is W and the defining k-invariants span the entire image of the Bockstein. We show that if p>dim V-dim W+1, then the mod p cohomology of G can be explicitly computed as an algebra. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Ausoni-Rognes/tcl_us Title: Algebraic K-theory of topological K-theory Author: Christian Ausoni Author2: John Rognes Email: ausoni@math.ethz.ch Email2: rognes@math.uio.no Abstract: Let l_p = BP<1>_p be the p-complete connective Adams summand of topological K-theory, and let V(1) be the Smith-Toda complex. For p>3 we explicitly compute the V(1)-homotopy of the algebraic K-theory spectrum of l_p. In particular we find that it is a free finitely generated module over the polynomial algebra P(v_2), except for a sporadic class in degree 2p-3. Thus also in this case algebraic K-theory increases chromatic complexity by one. The proof uses the cyclotomic trace map from algebraic K-theory to topological cyclic homology, and the calculation is actually made in the V(1)-homotopy of the topological cyclic homology of l_p. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Dwyer-Greenlees/CompleteTorsio n Complete modules and torsion modules by W. G. Dwyer and J. P. C. Greenlees Suppose that $R$ is a ring and that $A$ is a chain complex over $R$. Inside the derived category of differential graded $R$-modules there are naturally defined subcategories of $A$-torsion objects and of $A$-complete objects. Under a finiteness condition on $A$, we develop a Morita theory for these subcategories, find conceptual interpretations for some associated algebraic functors, and, in appropriate commutative situations, identify the associated functors as local homology or local cohomology. Some of the results are suprising even in the case $R=Z$ and $A=Z/p$. Addresses: University of Notre Dame, Notre Dame, IN 46556, USA dwyer.1@nd.edu School of Mathematics and Statistics, Hicks Building, Sheffield S3 7RH. UK j.greenlees@sheffield.ac.uk 5. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Kuhn/kuhnsplit Stable Splittings and the Diagonal Nicholas J. Kuhn Department of Mathematics, University of Virginia, Charlottesville, VA 22903 njk4x@virginia.edu AMS classification numbers: Primary 55P35; Secondary 55P42 Many approximations to function spaces admit natural stable splittings, with a typical example being the stable splitting of a space C_d(X) approximating Omega^d Sigma^d X. With an eye towards understanding cup products in the cohomology of such function spaces, we describe how the diagonal interacts with the stable splitting. The description involves group theoretic transfers. In an appendix independent of the rest of the paper, we use ideas from Goodwillie calculus to show that such natural stable splittings are unique, and discuss three different constructions showing their existence. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Mahowald-Ravenel-Shick/telconj Title: The triple loop space approach to the telescope conjecture Authors: Mark Mahowald, Doug Ravenel, Paul Shick Addresses: Northwestern University, University of Rochester, John Carroll University email: mark@math.mwu.edu, drav@harpo.cc.rochester.edu, shick@jcu.edu AMS Classification: 55 Abstract: The purpose of this paper is to describe an unsuccessful attempt to prove that the telescope conjecture is false for all $n \ge 2$ and all primes $p$. At the time it was originally proposed over 20 years ago, the telescope conjecture appeared to be the simplest and most plausible statement about the relationship between two different localization functors. We hope that the present paper will show that this is no longer the case. We will set up a spectral sequence converging to the homotopy of one of the two localizations (the geometrically defined telescope) of a certain spectrum, and it will be apparent that only a bizarre pattern of differentials would lead to the known homotopy of the localization defined in terms of $BP$-theory. While we cannot exclude such a pattern, it is certainly not favored by Occam's razor. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Mahowald-Ravenel-Shick/temss Title: The Thomified Eilenberg-Moore spectral sequence Authors: Mark Mahowald, Doug Ravenel, Paul Shick Addresses: Northwestern University, University of Rochester, John Carroll University email: mark@math.mwu.edu, drav@harpo.cc.rochester.edu, shick@jcu.edu AMS Classification: 55 Abstract: We construct a generalization of the Eilenberg-Moore spectal sequence, which in some interesting cases turns out to be a form the Adams spectral sequence. We apply the spectral sequence to give a new construction of the $Z /p$-equivariant Adams spectral sequence of Greenlees. 9. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/McAuley/revised-hilbert This one has an abstract in .dvi form, so I do not include it. The title is A Proof of the Hilbert-Smith Conjecture by Louis F. McAuley (The Hilbert-Smith conjecture is the one about a topological group having to be a Lie group under certain conditions). ---------------------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< 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/pub/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.