------------------------------- 7 new papers this time, from Bokstedt-Ottosen, Chataur-Scherer, Hung, Jardine, Rosu (2), and Ruiz-Viruel. Mark Hovey New papers appearing on hopf between 1/21/03 and 03/01/03 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Bokstedt-Ottosen/stringV4 Title: A spectral sequence for string cohomology Authors: Marcel Bokstedt and Iver Ottosen AMS Classification numbers: 55N91, 55P35, 18G50 Address of Authors: Institut for Matematiske Fag Aarhus Universitet Ny Munkegade DK-8000 Aarhus C Matematisk Afdeling Koebenhavns Universitet Universitetsparken 5 DK-2100 Koebenhavn OE Email address of Authors: marcel@imf.au.dk iver@math.ku.dk Abstract: Let $X$ be a 1-connected spaces with free loop space $\Lambda X$. We introduce two spectral sequences converging towards $H^*(\Lambda X;\ZZ /p)$ and $H^*((\Lambda X)_{hS^1};\ZZ /p)$. The $E_2$-terms are certain non Abelian derived functors applied to $H^*(X;\ZZ /p)$. When $H^*(X;\ZZ /p)$ is a polynomial algebra, the spectral sequences collapse for more or less trivial reasons. If $X$ is a sphere it is a surprising fact that the spectral sequences collapse for $p=2$. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Chataur-Scherer/fibrewise Fibrewise nullification and the cube theorem David Chataur and Jerome Scherer CRM Barcelona, dchataur@crm.es Universidad Autonoma de Barcelona, jscherer@mat.uab.es Our aim is to construct fibrewise localizations in model categories. For pointed spaces, the general idea is to decompose the total space of a fibration as a diagram over the category of simplices of the base and replace it by the localized diagram. This of course is not possible in an arbitrary category. We have thus to adapt another construction which heavily depends on Mather's cube theorem. Working with model categories in which the cube theorem holds, we characterize completely those who admit a fibrewise nullification. As an application we get fibrewise plus-construction and fibrewise Postnikov sections for algebras over an operad. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Hung/HungMZ99 Title of Paper: The weak conjecture on spherical classes Author: Nguy\^{e}n H. V. Hung 1991 Mathematics Subject Classification: Primary 55P47, 55Q45, 55S10, 55T15. Address of Author: Department of Mathematics, Vietnam National University, Hanoi, 334 Nguyen Trai Street, Hanoi, Vietnam E-mail address: nhvhung@vnu.edu.vn Abstract: Let $A$ be the mod 2 Steenrod algebra. We construct a chain-level representation of the dual of Singer's algebraic transfer, $$ Tr_k^*: Tor^A_k(F_2,F_2) \to F_2\otimes_A F_2[x_1,...,x_k], $$ which maps Singer's invariant-theoretic model of the lambda algebra to $F_2[x_1^{\pm},...,x_k^{\pm}]$ and is the inclusion of the Dickson algebra into the polynomial algebra $F_2[x_1,...,x_k]$. Based on this chain-level representation, we study some aspects of the weak conjecture on spherical classes and prove it in some special cases. (Address of Paper: Math. Zeit. 231 (1999), 727-743) 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Jardine/simpset3 Abstract: "Simplicial approximation", by J.F. Jardine This paper displays an approach to the construction of the homotopy theory of simplicial sets and the corresponding equivalence with the homotopy theory of topological spaces which is based on simplicial approximation techniques. The required simplicial approximation results for simplicial sets and their proofs are given in full. Subdivision behaves like a covering in the context of the techniques displayed here. Department of Mathematics University of Western Ontario London, Ontario N6A 5B7 Canada E-mail: jardine@uwo.ca URL: http://www.math.uwo.ca/~jardine/papers/ 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Rosu/ellc Title: Equivariant Elliptic Cohomology and Rigidity Author: Ioanid Rosu, AMS Classification numbers: 55N34; 55N91 xxx LANL archive ID number: AT/9912089 Addresses and emails of Authors: Ioanid Rosu, M.I.T., Cambridge, MA. ioanid@math.mit.edu Equivariant elliptic cohomology with complex coefficients was defined axiomatically by Ginzburg, Kapranov and Vasserot and constructed by Grojnowski. We give an invariant definition of S^1-equivariant elliptic cohomology, and use it to give an entirely cohomological proof of the rigidity theorem of Witten for the elliptic genus. We also state and prove a rigidity theorem for families of elliptic genera. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Rosu/kt Title: Equivariant K-theory and Equivariant Cohomology Author: Ioanid Rosu, with an appendix by Allen Knutson and Ioanid Rosu AMS Classification numbers: 55N91 xxx LANL archive ID number: AT/9912088 Addresses and emails of Authors: Ioanid Rosu, M.I.T., Cambridge, MA. ioanid@math.mit.edu Allen Knutson, University of California at Berkeley, CA allenk@math.berkeley.edu For T an abelian compact Lie group, we give a description of T-equivariant K-theory with complex coefficients in terms of equivariant cohomology. In the appendix we give applications of this by extending results of Chang-Skjelbred and Goresky-Kottwitz-MacPherson from equivariant cohomology to equivariant K-theory. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Ruiz-Viruel/rv TITLE: The classification of $p$-local finite groups over the extraspecial group of order $p^3$ and exponent $p$. AUTHORS: Albert Ruiz, LAGA Universit{\'e} Paris XIII 99av J.B.\ Cl{\'e}ment 93430 Villetaneuse France ruiz@math.univ-paris13.fr Antonio Viruel Dpto de {\'A}lgebra, Geometr{\'\i}a y Topolog{\'\i}a Universidad de M{\'a}laga Apdo correos 59 29080 M{\'a}laga Spain viruel@agt.cie.uma.es ABSTRACT: The concept of $p$-local finite group arise in the work of Broto-Levi-Oliver as a generalization of the classical concept of finite group. Therefore, the classification of $p$-local finite groups has interest, not only by itself but, as an opportunity to enlighten one of the highest mathematical achievements in the last decades: The Classification of Finite Simple Groups. In this work we classify all $p$-local finite group over the $p$-groups of type $p^{1+2}_+$. In this classification three new exotic $7$-local finite groups arise. ---------------