Happy New Year! I remind you that your abstracts must contain your name and the title of the paper at a minimum. I have had to add these in by hand in a couple of recent cases. 7 new papers this time, from BrownR-Higgins, Jiang, Luo, Madsen-Weiss (the proof of the Mumford conjecture!), MauerOats, McClure-SmithJH, and Symonds. Mark Hovey New papers appearing on hopf between 12/01/02 and 01/08/03 1. http://hopf.math.purdue.edu/cgi-bin/generate?/BrownR-Higgins/cubabgp3 Title of Paper: Cubical abelian groups with connections\\ are equivalent to chain complexes Author(s): Ronald Brown and Philip J. Higgins AMS Classification numbers xxx LANL archive: math.AT/0212157 Addresses of Authors: Ronald Brown Mathematics Division \\ School of Informatics, \\ University of Wales, Bangor \\Gwynedd LL57 1UT, U.K. Philip J. Higgins, Department of Mathematical Sciences, \\ Science Laboratories, \\ South Rd., \\ Durham, DH1 3LE, U.K Email address of Authors r.brown@bangor.ac.uk p.j.higgins@durham.ac.uk Abstract: The theorem of the title is deduced from the equivalence between crossed complexes and cubical $\omega$-groupoids with connections proved by the authors in 1981. In fact we prove the equivalence of five categories defined internally to an additive category with kernels. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Jiang/realization Title of Paper: On the realization of the unstable modules Author: JIANG Dong Hua AMS Classification numbers: 55N99, 55S10 math.AT/0212054 Address of Author: LAGA, Institut Galilee, UMR 7539 University Paris Nord, Avenue Jean-Baptiste Clement 93430 VILLETANEUSE, FRANCE Email address of Author: donghua.jiang@m4x.org In this article, we give some restrictions about the structure of an unstable module, which should be verified providing this module is the reduced mod 2 cohomology of a space or a spectrum. We begin by studing the structure of the sub-modules of \Sigma^s H^\ast(B(Z/2)^{\oplus d}; Z/2)^{\oplus \alpha_d} (s \geq 0, \alpha_d > 0), i.e., the unstable modules whose nilpotent filtration has length 1. Next, we generelise this result for the unstable modules whose nilpotent filtration has a finite length, and who verified an additional condition. The result says that under some hypothesis, the reduced mod 2 cohomology of a space or a spectrum does not have arbitrary big gaps in its structure. This result is obtained by applying the famous Adams' theorem about the Hopf invariant and the classification of the injective unstable modules. For the unstable modules satisfing the condition of the theorem 3 (for example, any suspension of a sub-module of H^\ast(B(Z/2)^{\oplus d}; Z/2)^{\oplus \alpha_d}, the theorem 3 gives the upper bound of the length of the gaps in the modules, which means the module does not contain arbitrary big gaps. So when the module is reduced satisfing the condition of the theorem 4, its weight should be infinite. This gives us so many examples of the non-realizable unstable modules: F(n), any tensor product of F(n_i), etc. (These examples can also be proved by the theorem of Lionel Schwartz about the Kuhn conjecture, which was generalised by F-X. Dehon - G. Gaudens.) This article is written in french and the work is done under the direction of L. Schwartz. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Luo/pre 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. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Madsen-Weiss/mumf The stable moduli space of Riemann surfaces: Mumford's conjecture Ib Madsen and Michael Weiss AMS classification numbers 57R50; 14H15, 32G15, 57R45, 57M99 Submitted to arXiv: math.AT/0212321 Institute for the Mathematical Sciences Aarhus University 8000 Aarhus C Denmark Department of Mathematics University of Aberdeen Aberdeen AB24 3UE United Kingdom imadsen@imf.au.dk m.weiss@maths.abdn.ac.uk The main result of this paper amounts to a complete evaluation of the integral cohomological structure of the stable mapping class group (i.e, the group of isotopy classes of automorphisms of a connected oriented surface of "large" genus). In particular it verifies the conjecture of D.Mumford about the rational cohomology of the stable mapping class group. It is part of a more recent development in the field which began with Ulrike Tillmann's result (Invent. Math., 1997) that the plus construction makes the classifying space of the stable mapping class group into an infinite loop space. This led to a stable homotopy theory version of Mumford's conjecture, stronger than the original (Madsen and Tillmann, Invent. Math., 2001). We prove the extended version of Mumford's conjecture by a mixture of techniques from singularity theory and from homotopy theory. The stability theorem of J.Harer (Annals of Math., 1985) and the "First Main theorem" of V.Vassiliev ("Complements of Discriminants of smooth maps: Topology and Applications", Trans. of Math. Monographs Vol.98, revised edition, Amer. Math. Soc. 1994) are prominent components of our proof. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/MauerOats/algebraic-calc Algebraic Goodwillie calculus and a cotriple model for the remainder Andrew Mauer-Oats We define an ``algebraic'' version of the Goodwillie tower, P_n^alg F(X), that depends only on the behavior of F on coproducts of X. When F is a functor to connected spaces or grouplike H-spaces, the functor P_n^alg F is the base of a fibration whose fiber is the simplicial space associated to a cotriple built from the (n+1) cross effect of the functor F. When the connectivity of X is large enough (for example, when F is the identity functor and X is connected), the algebraic Goodwillie tower agrees with the ordinary (topological) Goodwillie tower, so this theory gives a way of studying the Goodwillie approximation to a functor F in many interesting cases. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/McClure-SmithJH/McClureSmith2_1 Multivariable cochain operations and little $n$-cubes. James E. McClure and Jeffrey H. Smith 18D50, 55P48, 16E40 math.QA/0106024 Department of Mathematics Purdue University 150 N. University Street West Lafayette, IN 47907-2067 mcclure@math.purdue.edu jhs@math.purdue.edu This is a revision of a paper first posted June 4, 2001. It will appear in the Journal of the AMS. In this paper we construct a small $E_\infty$ chain operad $\S$ which acts naturally on the normalized cochains $S^*X$ of a topological space. We also construct, for each $n$, a suboperad $\S_n$ which is quasi-isomorphic to the normalized singular chains of the little $n$-cubes operad. The case $n=2$ leads to a substantial simplification of our earlier proof of Deligne's Hochschild cohomology conjecture. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Symonds/morava The Tate-Farrell cohomology of the Morava Stabilizer Group $S_{p-1}$ with coefficients in $E_{p-1}$ Peter Symonds We calculate the Tate-Farrell cohomology of the Morava stabilizer group $S_{p-1}$ with coefficients in the moduli space $E_{p-1}$ for odd primes $p$. ------------