-------------------------------- Notice that Hopf now has a web form for submitting papers. As one of the maintainers, I can tell you that it is much easier for me if you use this web form (or ftp) to submit your papers to Hopf rather than email. The human factor (i.e., me) still causes the most delays in announcements of papers. There are 9 new papers this time, from BrownR-Janelidze, BrownR-Wensley, Cisinski, Devinatz-Hopkins, Dugger-Shipley, Kitchloo-Notbohm, Libman, Mauger, and Morava. Mark Hovey New papers appearing on hopf between 07/18/02 and 09/11/02 1. http://hopf.math.purdue.edu/cgi-bin/generate?/BrownR-Janelidze/dgpsmap Title: Galois theory and a new homotopy double groupoid of a map of spaces Author(s): R. Brown, G.Janelidze AMS Classification numbers: 18D05, 20L05, 55 Q05, 55Q35 R. Brown, Mathematics Division, School of Informatics, University of Wales, Dean St., Bangor, Gwynedd LL57 1UT, U.K. G.Janelidze, Mathematics Institute, Georgian Academy of Sciences, Tbilisi, Georgia. r.brown@bangor.ac.uk,george_janelidze@hotmail.com The authors have used generalised Galois Theory to construct a homotopy double groupoid of a surjective fibration of Kan simplicial sets. Here we apply this to construct a new homotopy double groupoid of a map of spaces, which includes constructions by others of a 2-groupoid, cat1-group or crossed module. An advantage of our construction is that the double groupoid can give an algebraic model of a foliated bundle. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/BrownR-Wensley/crossed-modules Title of Paper: Computation and Homotopical Applications of Induced Crossed Modules Authors: Ronald Brown \\ Christopher D Wensley AMS Classification numbers: 55P10,55Q2,20L05 Addresses of Authors: Mathematics Division, School of Informatics, University of Wales, Bangor Gwynedd, LL57 1UT U.K. {r.brown,~c.d.wensley}@bangor.ac.uk We explain how the computation of induced crossed modules allows the computation of certain homotopy 2-types and, in particular, second homotopy groups. We discuss various issues involved in computing induced crossed modules and give some examples and applications. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Cisinski/top Théories homotopiques dans les topos Denis-Charles Cisinski Primary 18G55 (Homotopical Algebra) 18F20 (Presheaves and Sheaves) Secondary 18E35 (Localization of Categories) 18B25 (Topoi) 18G30 (Simplicial Objects) Submitted to the J. Pure Appl. Algebra Address Institut de Mathématiques de Jussieu Université Paris 7 2, place jussieu 75251 Paris cedex O5 France cisinski@math.jussieu.fr The purpose of these notes is to give an ad hoc construction of a closed model category structure on a topos inverting an arbitrary small set of arrows. Moreover, a necessary and sufficient condition for those structures to be proper is given. As an example, the Joyal closed model category structure on the category of simplicial objects of a topos is constructed without the use of (boolean) points. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Devinatz-Hopkins/homotopy-fixed-point This is an updated version of the paper whose abstract follows. Title: Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups Author: Ethan S. Devinatz and Michael J. Hopkins Addresses of Authors: Ethan S. Devinatz Department of Mathematics University of Washington Seattle, WA 98195 Michael J. Hopkins Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02135 Email: devinatz@math.washington.edu mjh@math.mit.edu Let G be a closed subgroup of the semi-direct product of the nth Morava stabilizer group with the Galois group of the field extension of degree n of the field of p elements. We construct a "homotopy fixed point spectrum" whose homotopy fixed point spectral sequence involves the continuous cohomology of G. These spectra have the expected functorial properties and agree with the Hopkins-Miller fixed-point spectra when G is finite. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Dugger-Shipley/kdeqDS Title: K-theory and derived equivalences Authors: Daniel Dugger and Brooke Shipley AMS Math. Subj. Class. 19D99, 18E30, 55U35 Department of Mathematics, University of Oregon, Eugene, OR 97403 email: ddugger@math.uoregon.edu Department of Mathematics, Purdue University, West Lafayette, IN 47907 email: bshipley@math.purdue.edu Abstract: We show that two rings have the same algebraic K-theory if their derived categories are triangulated-equivalent. Similar results are given for G-theory, and for the `compact K-theory' of a large class of abelian categories. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Kitchloo-Notbohm/loopspacemanifold Authors: Nitu Kitchloo and Dietrich Notbohm Ttile: Quasi finite loop spaces are manifolds It is an old conjecture, that finite $H$-spaces are homotopy equivalent to manifolds. Here we prove that this conjecture is true for loop spaces. Actually, we show that every quasi finite loop space is equivalent to a stably parallelizable manifold. The proof is conceptual and relies on the theory of p-compact groups. On the way we also give a complete classification of all simple 2-compact groups of rank 2. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Libman/towers Title: Tower techniques for cofacial resolutions author: A. Libman Classification: 55U35,55T15,18A25 Address: Dept. of Math. Sciences, University of Aberdeen, Aberdeen AB24 3UE, UK. E-mail: assaf@maths.abdn.ac.uk Let $J$ be a continuous coaugmented functor on spaces. For every space $X$ one constructs a cofacial resolution $X \to J^\bullet X$ (namely a cosimplicial resolution without its codegeneracy maps) in the usual way. Following Bousfield and Kan, one defines $J_s(X) = tot_s J^\bullet X$. Suppose $D$ is a small category and that $X$ is a $D$-diagram of $J$-injective spaces, namely $X(d) \to JX(d)$ admits a left inverse for every object $d$ in $D$, but in a way which need not be compatible, namely a map $JX \to X$ cannot be constructed out of this data. We show that for many free diagrams $F$, the spaces $hom_D(F,X)$ are $J_s$-injective for $s<\infty$. Thus, the functors $\mathbb{Z}_s$ of Bousfield and Kan capture a large class of polyGEMs as their injective spaces. This generalises earlier results by the author. Our methods use pro-object arguments, which are originally due to Farjoun. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/Mauger/hopf_alg_pgroups The Cohomology of certain Hopf Algebras Associated with p-Groups Justin Mauger AMS Classification numbers: 16E40, 16S37 2033 Sheridan Road Northwestern University Evanston, IL 60208 justin@math.northwestern.edu In this paper, we study the cohomology H^*(A)=Ext_A^*(k,k) of a locally finite, connected, cocommutative Hopf algebra A over k=F_p. Specifically, we are interested in those algebras A for which H^*(A) is generated as an algebra by H^1(A) and H^2(A). We shall call such algebras \emph{semi-Koszul}. Given a central extension of Hopf algebras $F\lra A\lra B$ with $F$ monogenic and $B$ semi-Koszul, we use the Cartan-Eilenberg spectral sequence and algebraic Steenrod operations to determine conditions for $A$ to be semi-Koszul. Special attention is given to the case in which $A$ is the restricted universal enveloping algebra of the Lie algebra obtained from the mod-$p$ lower central series of a $p$-group. We show that the algebras arising in this way from extensions by $\z$ of an abelian $p$-group are semi-Koszul. Explicit calculations are carried out for algebras arising from rank 2 $p$-groups. 9. http://hopf.math.purdue.edu/cgi-bin/generate?/Morava/orbiHKR Author: Jack Morava Title: HKR characters and higher twisted sectors This is the writeup of an expository talk, presented at the ChengDu (Sichuan) ICM Satellite conference on stringy orbifolds. It is intended as an introduction to the work of Hopkins, Kuhn, and Ravenel on generalized group characters, which seems to fit very well with the theory of what physicists call higher twisted sectors in the theory of orbifolds.