Subject: new Hopf listings From: Mark Hovey Date: 08 Apr 1999 07:18:37 -0400 5 new papers this time, including a classic that has never been publicly available before (Mike Boardman's conditionally convergent spectral sequences). Mark Hovey New papers uploaded to hopf between 3/22/99 and 4/8/99. 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Bisson-Pengelley-Williams/stab lops Stabilizing the lower operations for mod 2 cohomology Terrence P. Bisson Canisius College, Buffalo, NY 14208 bisson@canisius.edu David J. Pengelley New Mexico State University Las Cruces, NM 88003} davidp@nmsu.edu Frank Williams New Mexico State University Las Cruces, NM 88003} frank@nmsu.edu Primary 55S99; Secondary 16W30, 16W50, 55S10, 57T05 In {Bisson-Joyal} and {Pengelley-Williams} we studied a bialgebra K which underlies both the Steenrod algebra and the Dyer-Lashof algebra. Its elements act as lower-indexed operations in both the mod 2 cohomology of spaces and the mod 2 homology of infinite loop spaces. The algebra K can be defined explicitly by generators and relations {Pengelley-Williams}, or it can be defined as the algebra of operations in the theory of Q-modules {Bisson-Joyal}. In {Pengelley-Williams} a connection between K and the Steenrod algebra A of stable cohomology operations was established by means of a sheared algebra bijection between A and a new algebra K^{(\infty )}, which is a stabilized version of K. In {Bisson-Joyal} the extended Milnor Hopf algebra M is used (among other purposes) to define a convolution algebra containing both K and A. In this paper we establish a connection between these two approaches. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Boardman/ccspseq Title: Conditionally Convergent Spectral Sequences Author: J. Michael Boardman Address: Department of Mathematics, Johns Hopkins University, 3400 N. Charles St., Baltimore MD 21218-2686 MSC Classification: 55T05 E-mail: boardman@math.jhu.edu Abstract: Convergence criteria for spectral sequences are developed that apply more widely than the traditional concepts. In the presence of additional conditions that depend on data internal to the spectral sequence, they lead to satisfactory convergence and comparison theorems. The techniques apply to whole-plane as well as half-plane spectral sequences. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/McAuley/hs Author: Louis F. McAuley Title: A Proof of the Hilbert-Smith Conjecture E-mail: louis@math.binghamton.edu The Hilbert-Smith conjecture is that if G is a locally compact group which acts effectively on a compact connected n-manifold M as a topological transformation group, then G is a Lie group. If G is not a Lie group, then G contains a group isomorphic to a p-adic group A_p which acts effectively on M. It is shown in this paper that A_p can not act effectively on M and, consequently, the Hilbert-Smith Conjecture is true. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Notbohm/finob THE FINITENESS OBSTRUCTION FOR LOOP SPACES Author: Dietrich Notbohm AMS class.: 57Q12, 55R35, 55R10 Address: Mathematisches Institut Universität Göttingen Bunsenstr. 3-5 37073 Göttingen Germany e-mail: notbohm@cfgauss.uni-math.gwdg.de For finitely dominated spaces, Wall constructed a finiteness obstruction, which decides whether a space is equivalent to a finite $CW$-complex or not. It was conjectured that this finiteness obstruction always vanishes for quasi finite $H$-spaces, that are $H$-spaces whose homology looks like the homology of a finite $CW$-complex. In this paper we prove this conjecture for loop spaces. In particular, this shows that every quasi finite loop space is actually homotopy equivalent to a finite $CW$-complex. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Simpson/giraudH Title: A Giraud-type characterization of the simplicial categories associated to closed model categories as $\infty$-pretopoi Author: Carlos Simpson Address: CNRS UMR 5580, Laboratoire Emile Picard, Universite Paul Sabatier, 31062 Toulouse CEDEX, France Email: carlos@picard.ups-tlse.fr Abstract: Theorem (after Giraud, SGA 4): Suppose $A$ is a simplicial category. The following conditions are equivalent: (i) There is a cofibrantly generated closed model category $M$ such that $A$ is equivalent to the Dwyer-Kan simplicial localization $L(M)$; (ii) $A$ admits all small homotopy colimits, and there is a small subset of objects of $A$ which are $A$-small, and which generate $A$ by homotopy colimits; (iii) There exists a small $1$-category $C$ and a morphism $g:C\rightarrow A$ sending objects of $C$ to $A$-small objects, which induces a fully faithful inclusion $i:A\rightarrow \widehat{C}$, such that $i$ admits a left homotopy-adjoint $\psi$. We call a Segal category $A$ which satisfies these equivalent conditions, an {\em $\infty$-pretopos}. Note that (i) implies that $A$ admits all small homotopy limits too. If furthermore there exists $C\rightarrow A$ as in (iii) such that the adjoint $\psi$ preserves finite homotopy limits, then we say that $A$ is an ``$\infty$-topos''. ---------------------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 (Mosaic, Netscape) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to conference announcements, 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/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. ------- End of forwarded message -------