Subject: new Hopf listings Date: 05 Jan 2004 16:43:25 -0500 From: Mark Hovey Reply-To: mhovey@wesleyan.edu To: dmd1@lehigh.edu Happy New Year! This is the beginning of the 10th year I have been doing this. 10 new papers this time, from Bubenik, ChornyB (2), Gillespie, Hovey, Jardine, Lueck, Mitchell, Pengelley-Williams, and Vavpatic-Viruel. Mark Hovey New papers appearing on hopf between 11/25/03 and 1/05/04 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Bubenik/fsi Title: Free and semi-inert cell attachments Author: Peter Bubenik Author's e-mail address: peter.bubenik@epfl.ch AMS classification number: 55P35 (Primary) 16E45 (Secondary) arXive submission number: math.AT/0312387 Abstract: Let $Y$ be the space obtained by attaching a finite-type wedge of cells to a simply-connected, finite-type CW-complex. We introduce the free and semi-inert conditions on the attaching map which broadly generalize the previously studied inert condition. Under these conditions we determine $H_*(\Omega Y;R)$ as an $R$-module and as an $R$-algebra respectively. Under a further condition we show that $H_*(\Omega Y;R)$ is generated by Hurewicz images. As an example we study an infinite family of spaces constructed using only semi-inert cell attachments. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/ChornyB/Localization1 Title: Localization with respect to a class of maps I - Equivariant localization of diagrams of spaces Author: Boris Chorny Author's e-mail address: bchorny2@uwo.ca Abstract: Homotopical localizations with respect to a set of maps are known to exist in cofibrantly generated model categories (satisfying additional assumptions). In this paper we expand the existing framework, so that it will apply to not necessarily cofibrantly generated model categories and, more important, will allow for a localization with respect to a class of maps (satisfying some restrictive conditions). We illustrate our technique by applying it to the equivariant model category of diagrams of spaces. This model category is not cofibrantly generated. We give conditions on a class of maps which ensure the existence of the localization functor; these conditions are satisfied by any set of maps and by the classes of maps which induce ordinary localizations on the generalized fixed-points sets. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/ChornyB/Localization2 Title: Localization with respect to a class of maps II - Equivariant cellularization and its application Author: Boris Chorny Author's e-mail address: bchorny2@uwo.ca Abstract: We present an example of a homotopical localization functor which is not a localization with respect to any set of maps. Our example arises from equivariant homotopy theory. The technique of equivariant cellularization is developed and applied to the proof of the main result. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Gillespie/sheafproblem Title: The flat model structure on Ch(O) Author: James Gillespie Email: jrg21@psu.edu Abstract: Let Ch(O) be the category of chain complexes of O-modules on a topological space T (where O is a sheaf of rings on T ). We put a Quillen model structure on this category in which the cofibrant objects are built out of flat modules. More precisely, these are the dg-flat complexes. Dually, the fibrant objects will be called dg-cotorsion complexes. We show that this model structure is monoidal, solving the previous problem of not having any monoidal model structure on Ch(O). As a corollary, we have a general framework for doing homological algebra in the category O-MOD of O-modules. I.e., we have a natural way to define the functors Ext and Tor in O-MOD. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Hovey/morava-E-operations Operations and co-operations in Morava $E$-theory Mark Hovey Wesleyan University mhovey@wesleyan.edu In this paper, we revisit the calculations of the operations and co-operations in Morava E-theory. Recall that the co-operations are the continuous functions from a profinite group G that is a version of the Morava stabilizer group to E_*. The operations are the completed twisted group ring E_*[[G]]. These results have appeared in the literature before. The advantage of this paper is that it is self-contained, works out all the details that are usually skipped over, and uses a new approach, not directly dependent on Morava's Annals paper on comodules, that the author finds fairly simple and elegant. Most of all, though, the author wrote this paper because he was unable to understand the proofs in the literature. He hopes it will be useful for people in the same unhappy situation. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Jardine/cat5 Categorical homotopy theory J.F. Jardine This paper is an exposition and extension of the ideas and methods of Cisinksi, set at the level of A-presheaves on a small Grothendieck site, where A is an arbitrary test category in the sense of Grothendieck. The model structures for the category of simplicial presheaves and all of its localizations can be modelled by A-presheaves in the sense that there is a corresponding model structure for A-presheaves with an equivalent homotopy category. The theory specializes, for example, to the homotopy theories of cubical sets, cubical presheaves, and gives a cubical model for motivic homotopy theory. The applications of Cisinski's ideas are explained in some detail for cubical sets. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Lueck/lueck_classifyingspaces1203 Title: Survey on Classifying Spaces for Families of Subgroups Author: Wolfgang Lueck AMS Classification numbers: 55R35, 57S99, 20F65, 18G99 Address: Mathematisches Institut der Westfaelischen Wilhelms Universitaet Einsteinstr. 62 48149 Muenster Germany Abstract: We define for a topological group G and a family of subgroups F two versions for the classifying space for the family F, the G-CW-version E_F(G) and the numerable G-space version J_F(G). They agree if G is discrete, or if G is a Lie group and each element in F compact, or if G is totally disconnected and F is the family of compact subgroups or of compact open subgroups. We discuss special geometric models for these spaces for the family of compact open groups in special cases such as almost connected groups G and word hyperbolic groups G. We deal with the question whether there are finite models, models of finite type, finite dimensional models. We also discuss the relevance of these spaces for the Baum-Connes Conjecture about the topological K-theory of the reduced group C^*-algebra, for the Farrell-Jones Conjecture about the algebraic K- and L-theory of group rings, for Completion Theorems and for classifying spaces for equivariant vector bundles and for other situations. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/Mitchell/sw Author: Stephen A. Mitchell Title: Stiefel-Whitney classes, united K-theory and real embeddings of number rings e-mail: mitchell@math.washington.edu We study the relations among the Stiefel-Whitney classes associated to the real embeddings of a number ring. Our results depend on a computation of the real and self-conjugate K-theory of the algebraic K-theory spectrum of the number ring. 9. http://hopf.math.purdue.edu/cgi-bin/generate?/Pengelley-Williams/subsmalg Global Structure of the mod 2 Symmetric Algebra over the Steenrod algebra. David J. Pengelley (davidp@nmsu.edu) Frank Williams (frank@nmsu.edu) The algebra S of symmetric invariants over the field with two elements is an unstable algebra over the Steenrod algebra A and is isomorphic to the mod two cohomology of BO, the classifying space for vector bundles. We provide a minimal presentation for S in the category of unstable A-algebras, i.e., a minimal set of generators and a minimal set of relations. From this we produce minimal presentations for various unstable A-algebras associated with the cohomology of related spaces, such as the BO(2^n - 1) that classify finite dimensional vector bundles, and the connected covers of BO. The presentations then show that certain of these unstable A-algebras coalesce to produce the mod 2 Dickson algebras, and we speculate about possible related topological realizability. Our methods also produce a related simple A-module presentation of the cohomology of infinite-dimensional real projective space, with a filtration having well-known filtered quotients. 10. http://hopf.math.purdue.edu/cgi-bin/generate?/Vavpetic-Viruel/PU On the mod p cohomology of BPU(p) Ales Vavpetic Fakulteta za matematiko in fiziko Univerza v Ljubljani Jadranska 19 SI-1111 Ljubljana Slovenia ales.vavpetic@fmf.uni-lj.si Antonio Viruel Dpto de Algebra, Geometria y Topologia Universidad de Malaga Apdo correos 59 E29080 Malaga Spain viruel@agt.cie.uma.es AMS Classification numbers: 55R35, 55P15 ABSTRACT: We study the mod p cohomology of the classifying space of the projective unitary group PU(p). We first proof that old conjectures due to J.F. Adams, and Kono and Yagita about the structure of the mod p cohomology of classifying space of connected compact Lie groups held in the case of PU(p). Finally, we proof that the classifying space of the projective unitary group PU(p) is determined by its mod p cohomology as an unstable algebra over the Steenrod algebra for p>3, completing previous works of Dwyer, Miller, Wilkerson at prime 2 and Broto, Viruel at prime 3. ---------------------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.