Subject: new Hopf listings Date: 06 Apr 2004 16:28:17 -0400 From: Mark Hovey 4 new papers this month, from Badzioch-Chung-Voronov, Broto-Castellana-Grodal-Levi-Oliver, Christensen-Isaksen, and KrauseH. Mark Hovey New papers appearing on hopf between 3/1/04 and 4/5/04 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Badzioch-Chung-Voronov/bcv Title: Yet another delooping machine Authors: Bernard Badzioch, Kuerak Chung, and Alexander A. Voronov Author's e-mail address: voronov@math.umn.edu Authors' mailing address: School of Mathematics, University of Minnesota, Minneapolis, MN 55455 Included ps or eps files: mor.eps AMS classification number: 55P48 (Primary); 18C10 (Secondary) ArXiv submission number: math.AT/0403098 Abstract: We suggest a new delooping machine, which is based on recognizing an n-fold loop space by a collection of operations acting on it, like the traditional delooping machines of Stasheff, May, Boardman-Vogt, Segal, and Bousfield. Unlike in the traditional delooping machines, which carefully select a nice space of such operations, we consider all natural operations on n-fold loop spaces, resulting in the algebraic theory Map (V_. S^n, V_. S^n). The advantage of this new approach is that the delooping machine is universal in a certain sense, the proof of the recognition principle is more conceptual, works the same way for all values of n, and does not need the test space to be connected. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Broto-Castellana-Grodal-Levi-Oliver/bcglo1 Subgroup families controlling $p$-local finite groups by C. Broto, N. Castellana, J. Grodal, R. Levi, B. Oliver A $p$-local finite group consists of a finite $p$-group $S$, together with a pair of categories which encode ``conjugacy'' relations among subgroups of $S$, and which are modelled on the fusion in a Sylow $p$-subgroup of a finite group. It contains enough information to define a classifying space which has many of the same properties as $p$-completed classifying spaces of finite groups. In this paper, we examine which subgroups control this structure. More precisely, we prove that the question of whether an abstract fusion system $F$ over a finite $p$-group $S$ is saturated can be determined by just looking at smaller classes of subgroups of $S$. We also prove that the homotopy type of the classifying space of a given $p$-local finite group is independent of the family of subgroups used to define it, in the sense that it remains unchanged when that family ranges from the set of $F$-centric $F$-radical subgroups (at a minimum) to the set of $F$-quasicentric subgroups (at a maximum). Finally, we look at constrained fusion systems, analogous to $p$-constrained finite groups, and prove that they in fact all arise from groups. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Christensen-Isaksen/duality Duality and Pro-spectra J. Daniel Christensen and Daniel C. Isaksen jdc@uwo.ca isaksen@math.wayne.edu Keywords: Spectrum, pro-spectrum, Spanier-Whitehead duality, closed model category, colocalization Arxiv: math.AT/0403451 MSC-class: 55P42 (Primary); 55P25, 18G55, 55U35, 55Q55 (Secondary) Abstract: Cofiltered diagrams of spectra, also called pro-spectra, have arisen in diverse areas, and to date have been treated in an ad hoc manner. The purpose of this paper is to systematically develop a homotopy theory of pro-spectra and to study its relation to the usual homotopy theory of spectra, as a foundation for future applications. The surprising result we find is that our homotopy theory of pro-spectra is Quillen equivalent to the opposite of the homotopy theory of spectra. This provides a convenient duality theory for all spectra, extending the classical notion of Spanier-Whitehead duality which works well only for finite spectra. Roughly speaking, the new duality functor takes a spectrum to the cofiltered diagram of the Spanier-Whitehead duals of its finite subcomplexes. In the other direction, the duality functor takes a cofiltered diagram of spectra to the filtered colimit of the Spanier-Whitehead duals of the spectra in the diagram. We prove the equivalence of homotopy theories by showing that both are equivalent to the category of ind-spectra (filtered diagrams of spectra). To construct our new homotopy theories, we prove a general existence theorem for colocalization model structures generalizing known results for cofibrantly generated model categories. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/KrauseH/stable Title: The stable derived category of a noetherian scheme Author: Henning Krause E-mail: hkrause@math.upb.de Abstract: For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the subcategory of perfect complexes. Some applications are included, for instance an analogue of maximal Cohen-Macaulay approximations, a construction of Tate cohomology, and an extension of the classical Grothendieck duality. ---------------------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 can also use ftp, explained below. 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). 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, go to http://hopf.math.purdue.edu and use the web form. You can also use anonymous ftp as above. First 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.