Subject: new Hopf listings From: Mark Hovey Date: 15 Jul 2000 06:25:00 -0400 13 new papers this time. Mark Hovey New papers appearing on hopf between 6/16/00 and 7/16/00. 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/AlAgl-Brown-Steiner/multipleca t Multiple categories: the equivalence of a globular and a cubical approach Fahd A. A. Al-Agl, Ronald Brown, Richard Steiner math.CT/0007009 Fahd A. A. Al-Agl\\Um-Alqura University,\\ Makkah\\Saudi Arabia Ronald Brown, \\ School of Informatics, \\ Mathematics Division, \\ University o f Wales,\\ Bangor, Gwynedd LL57 1UT, \\ United Kingdom. Richard Steiner, \\ Department of Mathematics, \\ University of Glasgow, \\University Gardens, \\ Glasgow G12 8QW \\ United Kingdom r.brown@bangor.ac.uk r.steiner@maths.gla.ac.uk We show the equivalence of two kinds of strict multiple category, namely the well known globular omega-categories, and the cubical omega-categories with connections. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Arkowitz-Strom/TrivModF Homotopy Classes that are Trivial Mod F Martin Arkowitz (Martin.Arkowitz@Dartmouth.edu) Jeffrey Strom (Jeffrey.Strom@Dartmouth.edu) Dartmouth College If F is a collection of topological spaces, then a homotopy class \alpha in [X,Y] is called F-trivial if \alpha _* = 0: [A,X] --> [A,Y] for all A in F. In this paper we study the collection Z_{F}(X,Y) of all F-trivial homotopy classes in [X,Y] when F = S, the collection of spheres, F = M, the collection of Moore spaces, and F = \Sigma, the collection of suspensions. Clearly Z_{\Sigma}(X,Y) \subseteq Z_{\M}(X,Y) \subseteq Z_{\S}(X,Y), and we find examples of {\it finite complexes} X and Y for which these inclusions are strict. We are also interested in Z_{F}(X) = Z_{F}(X,X) which under composition has the structure of a semi-group with zero. We show that if X is a finite dimensional complex and F = S, M or \Sigma, then the semi-group Z_{F}(X) is nilpotent. More generally, the nilpotency of Z_{F}(X) is bounded above by the F-killing length of X, a new numerical invariant which equals the number of steps it takes to make X contractible by successively attaching cones on wedges of spaces in F, and this in turn is bounded above by the F-cone length of X. We then calculate or estimate the nilpotency of Z_{F}(X) when F = S, M or \Sigma for the following classes of spaces: (1) projective spaces (2) certain Lie groups such as SU(n) and Sp(n). The paper concludes with several open problems. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Arlettaz/Arlettaz-survey Title: Algebraic K-theory of rings from a topological viewpoint Author: Dominique Arlettaz Dominique Arlettaz, Institut de math\'ematiques, Universit\'e de Lausanne, CH-1015 Lausanne, Switzerland dominique.arlettaz@ima.unil.ch Abstract: This paper is a long survey providing the basic definitions of the algebraic K-theory of rings and an overview of the main classical theorems which have been obtained by arguments from algebraic topology (in particular by using methods from stable homotopy theory, group cohomology and Postnikov theory). It will appear in Publicacions Matem\`atiques. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Arlettaz-Ausoni-Mimura-Yagita/ Arlettaz-A-M-Y Title: Integral cohomology and Chern classes of the special linear group over the ring of integers Author1: Dominique Arlettaz Author2: Christian Ausoni Author3: Mamoru Mimura Author4: Nobuaki Yagita Author1: Dominique Arlettaz, Institut de math\'ematiques, Universit\'e de Lausanne, CH-1015 Lausanne, Switzerland Author2: Christian Ausoni, Departement Mathematik, HG, ETH-Zentrum, 8092 Z\"urich, Switzerland Author3: Mamoru Mimura, Department of Mathematics, Faculty of Science, Okayama University, Okayama, Japan 700 Author4: Nobuaki Yagita, Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan E-mail1: dominique.arlettaz@ima.unil.ch E-mail2: ausoni@math.ethz.ch E-mail3: mimura@math.okayama-u.ac.jp E-mail4: yagita@mito.ipc.ibaraki.ac.jp Abstract: This paper is devoted to the complete calculation of the additive structure of the 2-torsion of the integral cohomology of the infinite special linear group SL(Z) over the ring of integers Z. This enables us to determine the best upper bound for the order of the Chern classes of all integral and rational representations of discrete groups. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Casacuberta-Scherer/casasche Homological localizations preserve 1-connectivity by Carles Casacuberta and Jerome Scherer Universitat Autonoma de Barcelona Universite de Lausanne casac@mat.uab.es jerome.scherer@ima.unil.ch To appear in Contemporary Mathematics, Proceedings of the 1999 Arolla Conference on Algebraic Topology. Every generalized homology theory $E$ yields a localization functor $L$ that sends the $E$-equivalences to homotopy equivalences. We prove that if $X$ is any $1$-connected space, then $LX$ is also $1$-connected, for every generalized homology theory $E$. This is deduced from a result by Hopkins and Smith stating that if $K(\Z,2)$ is $E$-acyclic then $E$ is trivial. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Dugger/ddpres Title: Combinatorial Model Categories Have Presentations Author: Daniel Dugger Purdue University West Lafayette, IN 47906 Email: ddugger@math.purdue.edu We show that every combinatorial model category can be obtained---up to Quillen equivalence---by localizing a model category of diagrams of simplicial sets. This says that any combinatorial model category can be built up from a category of `generators' and a set of `relations' ---i.e., any combinatorial model category has a presentation. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Dugger/dduniv Title: Universal Homotopy Theories Author: Daniel Dugger Address: Purdue University West Lafayette, IN 47906 Email: ddugger@math.purdue.edu Abstract: Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations' into these universal gadgets. The paper develops this formalism and also discusses various applications, for instance to the study of homotopy colimits, the Dwyer-Kan theory of framings, and to the homotopy theory of schemes. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Goebel-Rodriguez-Shelah/locsim ple TITLE: Large localizations of finite simple groups AUTHORS: Ruediger Goebel, Jose L. Rodriguez, and Saharon Shelah R.Goebel@uni-essen.de, jlrodri@mat.uab.es, shelah@math.huji.ac.il ABSTRACT: A group homomorphism $\eta: H\to G$ is called a localization of $H$ if every homomorphism $\varphi : H\to G$ can be `extended uniquely' to a homomorphism $\Phi :G\to G$ in the sense that $\Phi \eta = \varphi$. Libman showed that a localization of a finite group need not be finite. This is exemplified by a well-known representation $A_n\to SO_{n-1}(\R)$ of the alternating group $A_n$, which turns out to be a localization for $n$ even and $n\geq 10$. Dror Farjoun asked if there is any upper bound in cardinality for localizations of $A_n$. In this paper we answer this question and prove, under the generalized continuum hypothesis, that every non abelian finite simple group $H$, has arbitrarily large localizations. This shows that there is a proper class of distinct homotopy types which are localizations of a given Eilenberg--Mac Lane space $K(H,1)$ for any non abelian finite simple group $H$. 9. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Mandell/finite Equivariant p-adic Homotopy Theory Michael A. Mandell mandell@math.uchicago.edu Let G be a finite group. We show that the cochain functor with coefficients in \FPbar is an equivalence between the p-adic G-equivariant homotopy category of finite type nilpotent G-spaces and a full subcategory of the homotopy category of diagrams of \einf \FPbar-algebras indexed on the orbit category of G. This turns out to be an easy consequence of Elmendorf's Theorem and Kan's work on diagrams in closed model categories plus the equivalence in the nonequivariant context. 10. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Morava/PGGravity Title: Pretty Good Gravity Author: Jack Morava (not yet on xxx, but will be soon) Address: Dept. of Mathematics, the Johns Hopkins Uniperversity e-mail address: jack@math.jhu.edu Abstract: A theory of topological gravity is a homotopy-theoretic representation of the Segal-Tillmann topologification of a two-category with cobordisms as morphisms. This note describes a relatively accessible example of such a thing, suggested by the wall-crossing formulas of Donaldson theory. [This is a writeup of a talk at the RIMS Symposium on algebraic geometry and integrable systems related to string theory, June 12-16, 2000.] 11. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Ravenel/first Title of paper: The first Adams-Novikov differential for the spectrum T(m) Author: Douglas C. Ravenel Address of Author: University of Rochester, Rochester, NY 14627 Email address of author: drav@math.rochester.edu Abstract: There are p-local spectra T(m) with $BP_{*}(T(m))=BP_{*}[t_{1},\dots ,t_{m}]$. In this paper we determine the first nontrivial differential in the Adams--Novikov spectral sequence for each of them for p odd. For m=0 (the sphere spectrum) this is the Toda differential, whose source has filtration 2 and whose target is the first nontrivial element in filtration 2p+1. The same goes for m=1, and for larger m the target is $v_2$ times the first such element. The proof uses the Thomified Eilenberg-Moore spectral sequence. 12. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Ravenel/micro Title of paper: The microstable Adams-Novikov spectral sequence Author: Douglas C. Ravenel Address of Author: University of Rochester, Rochester, NY 14627 Email address of author: drav@math.rochester.edu Abstract: In the Adams--Novikov spectral sequence one considers Ext groups over the Hopf algebroid $\Gamma =BP_{*}(BP)$. There are spectra $T(m)$ with $BP_{*} (T (m))=BP_{*}[t_{1},...,t_{m}]$, which leads one to replace $\Gamma $ by $\Gamma (m+1)=\Gamma / (t_{1},... ,t_{m})$. The corresponding Ext groups have certain structural features that are independent of $m$. In this paper we set up an algebraic framework for studying the limit as $m \to \infty $. In particular there is an analog of the chromatic spectral sequence in which the Morava stabilizer group gets replaced by an infinitesimal analog, hence the title. 13. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/SmithL/koszulii I can't read the abstract of this file, but I think this is not Larry's fault. Clarence is out of town though, and I am about to be, so I wanted to announce it now. It has to do with invariant theory of Z/p acting on a polynomial ring F[V]. The detailed abstract will appear next time. ---------------------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.