Subject: new Hopf listings Date: 24 Oct 2003 09:24:55 -0400 From: Mark Hovey Reply-To: mhovey@wesleyan.edu To: dmd1@lehigh.edu 10 new papers this time, from Dugger-Isaksen, Flores, Gaudens, Kitchloo-Wilson, Klein, LinJP, Luo, Nam, Sauvageot, and Schwede. Mark Hovey New papers appearing on hopf between 9/26/03 and 10/24/03 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Dugger-Isaksen/motcell Title: Motivic cell structures Authors: Daniel Dugger and Daniel C. Isaksen Authors' e-mail address: ddugger@math.uoregon.edu and isaksen@math.wayne.edu Abstract: An object in motivic homotopy theory is called cellular if it can be built out of motivic spheres using homotopy colimit constructions. We explore some examples and consequences of cellularity. We explain why the algebraic K-theory and algebraic cobordism spectra are both cellular, and prove some Kunneth theorems for cellular objects. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Flores/draft1 NULLIFICATION AND CELLULARIZATION OF CLASSIFYING SPACES OF FINITE GROUPS by RAM'ON J. FLORES Departamento de Matem'aticas, Universidad Aut'onoma de Barcelona, E-08193 Bellaterra, Spain E-mail address: ramonj@mat.uab.es Mathematical subject classification: 55P20, 55P80. Abstract. In this note we discuss the effect of the BZ/p-nullification and the BZ/p-cellularization functors over classifying spaces of finite groups, and we compare them with the corresponding ones with regard to Moore spaces, that have been intensively studied in the last years. We describe the BZ/p- nullification of BG by means of a Postnikov fibration, and we classify all finite groups G for which BG is BZ/p-cellular. In particular, we relate the effect these (co)localizations have over the fundamental group with the analogous functors in the category of groups. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Gaudens/bocksteinnul Title: A remark on N. Kuhn's unbounded strong realization conjecture Author(s): Gerald Gaudens Author's e-mail address: gaudens@math.univ-nantes.fr AMS classification number: 55S10; 57S35 Abstract: N. Kuhn has given several conjectures on the special features satisfied by the singular cohomology of topological spaces with coefficients in a finite prime field, as modules over the Steenrod algebra. The so-called Realization conjecture was solved in special cases By N. Kuhn and in complete generality by L. Schwartz. The more general Strong realization conjecture has been settled at the prime 2, as a consequence of the work of L. Schwartz, and the subsequent work of F.-X. Dehon and the author. In this note, we are interested in the even more general Unbounded strong realization conjecture. We shall prove that it holds at the prime $2$ for the class of spaces whose cohomology has a trivial Bockstein action in high degrees. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Kitchloo-Wilson/kitchloo-wilson Title: On fibrations related to real spectra Authors: Nitu Kitchloo and W. Stephen Wilson E-mail addresses: nitu@math.jhu.edu, wsw@math.jhu.edu Address: Department of Mathematics Johns Hopkins University Baltimore, Maryland 21218 Abstract: We consider real spectra, collections of Z/(2)-spaces indexed over Z direct sum Z_\alpha with compatibility conditions. We produce fibrations connecting the homotopy fixed points and the spaces in these spectra. We also evaluate the map which is the analogue of the forgetful functor from complex to reals composed with complexification. Our first fibration is used to connect the real 2^{n+2}(2^n-1)-periodic Johnson-Wilson spectrum ER(n) to the usual 2(2^n-1)-periodic Johnson-Wilson spectrum, E(n). Our main result is the fibration \Sigma^{\lambda(n)} ER(n) -> ER(n) -> E(n), where \lambda(n) = 2^{2n+1}-2^{n+2}+1. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Klein/embclass Title: On embeddings in the sphere Author: John R. Klein Author's e-mail address: klein@math.wayne.edu Abstract: We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification such embeddings in a wide range. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/LinJP/Lin=HspaceAnalog1 (This abstract was sent in dvi form; the program we use to convert is not perfect). H-spaces analogous to E8 mod 3 Dedicated to the memory of Masahiro Sugawara James P. Lin Department of Mathematics University of California, San Diego La Jolla, CA 92093-0112, U.S.A. email:jimlin@euclid.ucsd.edu Abstract: Let p be an odd prime. Let X0 be a finite, p-local, simply connected homotopy associative H-space. Suppose H* (X0; Zp) contains the subalgebra Zp [x0,_z0]_xp p(r0, P1 r0, Pp P1 r0, y0) 0, z0 satisfying z0 = Pp x0 = Q0Pp P1 r0, Pp P1 r0 = P1 y0 for r0 2 H3 (X0; Zp). The only known examples occur for p = 3 and involve the Lie group E8. In this note we prove that if X0 exists, then p must be 3. Thus there are no homotopy associative H-space analogues of E8mod 3 for primes bigger than 3. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Luo/pre (This is an updated version) Closed model categories for presheaves of simplicial groupoids and presheaves of 2-groupoids Zhi-ming Luo We prove that the category of presheaves of simplicial groupoids and the category of presheaves of 2-groupoids have Quillen closed model structures. We also show that the homotopy categories associated to the two categories are equivalent to the homotopy categories of simplicial presheaves and homotopy 2-types, respectively. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/Nam/transfer Title : Transfert alg'ebrique et repr'esentation modulaire du groupe lin'eaire Author : Tran Ngoc Nam Author's e-mail address : trngnam@hotmail.com Author's mailing address : LAGA, Universit'e Paris 13, 93430 Villetaneuse, France Abstract : On se propose de d'eterminer la dimension d'une repr'esentation du groupe lin'eaire d'efinie par un sous-espace vectoriel de l'alg`ebre `a puissances divis'ees, d'expliciter l'image du transfert alg'ebrique en degr'e g'en'erique et celle du transfert alg'ebrique quadruple, d'identifier les ind'ecomposables de degr'e pair de l'alg`ebre polynomiale `a 4 variables, vue comme module sur l'alg`ebre de Steenrod mod 2. 9. http://hopf.math.purdue.edu/cgi-bin/generate?/Sauvageot/thesis STABILISATION DES COMPLEXES CROISES Orin R. Sauvageot orin.sauvageot@epfl.ch Ecole Polytechnique Federale de Lausanne Institute of Mathematics This is my PhD thesis in FRENCH, 158 pages. The graphic files C-tensor-I.eps, pi-delta-4.eps and pi-xc.eps are included in the zip archives thesis-print.dvi.zip and thesis-screen.dvi.zip. (Note from Mark; you should get these eps files individually if you get the dvi file. The file thesis.dvi is thesis-print.dvi; thesis-screen.dvi is in case you have trouble viewing the diagrams in thesis.dvi on your screen. The files thesis.ps and thesis.pdf already have the eps files embedded) Abstract In this doctoral thesis we present a stabilization of the category of crossed complexes. Our work is motivated by the difficulty one has in performing algebraic calculations in Boardman's stable homotopy category, since products and actions are defined only up to homotopy in the underlying category of spectra, as defined by Bousfield and Friedlander. To correct this lack of precision, a number of new models of the stable homotopy category have been developed in which algebraic constructions are exactly defined. One such model is the category of symmetric spectra on simplicial sets, the manipulation of which is still not easy, however. The idea behind this thesis is to stabilize the category of crossed complexes, as it is an interesting approximation to the category of simplicial sets, reflecting certain, though not all, nonabelian homotopical information concerning simplicial sets. We have stabilized it according to the procedure codified in Hovey's "Spectra and symmetric spectra in general model categories". Stabilization requires that the category of crossed complexes satisfies certain properties. We have succeeded in proving these properties, in each case establishing a previously unknown result. For example, we have shown that it is cofibrantly generated and that it is a symmetric monoidal model category. Furthermore we have verified that it is a proper, cellular category. In proving the properness we have answered an open question posed by Brown and Golasinski. In the course of establishing these properties we have established a nonabelian version of the 5-Lemma. A crossed complex is a generalization of a chain complex of abelian groups. We have shown, however, that the stabilization of crossed complexes is homotopy equivalent to that of the category of chain complexes. On the other hand, the situation of unpointed crossed complexes is different, and it is very likely that their stabilization is not that of chain complexes. In order to argue so, we have constructed an innovative simplicial model of the Hopf map. It remains then to give a topological meaning to an unpointed stabilization. An attempt of answer is sketched. 10. http://hopf.math.purdue.edu/cgi-bin/generate?/Schwede/Morita Title: Morita theory in abelian, derived and stable model categories Author: Stefan Schwede e-mail address: sschwede@math.uni-muenster.de This is a survey paper, based on lectures given at the Workshop on "Structured ring spectra and their applications" which took place January 21-25, 2002, at the University of Glasgow. The term `Morita theory' is usually used for results concerning equivalences of various kinds of module categories. We focus on the covariant form of Morita theory, so the basic question is: When do two `rings' have `equivalent' module categories ? We discuss this question in different contexts and illustrate it by examples: (Classical) When are the module categories of two rings equivalent as categories ? (Derived) When are the derived categories of two rings equivalent as triangulated categories ? (Homotopical) When are the module categories of two ring spectra Quillen equivalent as model categories ? There is always a related question, which is in a sense more general: What characterizes the category of modules over a `ring' ? The answer is, mutatis mutandis, always the same: modules over a `ring' are characterized by the existence of a `small generator', which plays the role of the free module of rank one. The precise meaning of `small generator' depends on the context, be it an abelian category, a derived category or a stable model category. ---------------------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.