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4 new papers this time, from Bailey, Chebolu-Minac, 
Nguyen-Schwartz-Tran, and Ostvaer.  

                  Mark Hovey

New papers appearing on hopf between 11/20/08 and 3/9/09


1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bailey/bailey-bosmtmf

Title: 
On the spectrum bo \wedge tmf

Author(s): 
Scott M. Bailey

AMS classification number: 
55P10 (Primary) 55P42, 55Q51 (Secondary)

Abstract: 

M. Mahowald in his work on bo-resolutions, constructed a bo-module
splitting of the spectrum bo ^ bo into a wedge of summands related to
integral Brown-Gitler spectra.  In this paper, a similar splitting of
bo ^ tmf is constructed.  This splitting is then used to understand
the bo_*-algebra structure of bo_* tmf and allows for a description of
bo^* tmf.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Chebolu-Minac/Auslander-Reiten

Title:  Auslander-Reiten sequences for homotopists and arithmeticians
Authors: Sunil Chebolu, Jan Minac

Comments: 16 pages, to appear in "Annales des sciences math'ematiques du Quebec"

Abstract: We introduce Auslander-Reiten sequences for group algebras
and give several recent applications. The first part of the paper is
devoted to some fundamental problems in Tate cohomology which are
motivated by homotopy theory. In the second part of the paper we
interpret Auslander-Reiten sequences in the context of Galois theory
and connect them to some important arithmetic objects. 

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Nguyen-Schwartz-Tran/nguyen-schwartz-tran

Title: La fonction generatrice de Minc et une "conjecture de Segal" pour
       certains spectres de Thom

Authors: Nguyen Dang Ho Hai, Lionel Schwartz, Tran Ngoc Nam

Abstract

       On construit dans cet article une r'esolution injective minimale
 dans la cat'egorie U des modules instables sur l'alg`ebre de
 Steenrod modulo 2, de la cohomologie de certains spectres obtenus `a
 partir de l'espace de Thom du fibr'e, associ'e `a la repr'esentation
 r'eguli`ere r'eduite du groupe ab'elien 'el'ementaire (Z=2)n, au
 dessus de l'espace B(Z=2)n. Les termes de la r'esolution sont des
 produits tensoriels de modules de Brown-Gitler J(k) et de modules de
 Steinberg Ln introduits par S. Mitchell et S. Priddy.  Ces modules
 sont injectifs d'apr`es J. Lannes et S. Zarati, de plus ils sont
 ind'ecomposables. L'existence de cette r'esolution avait 'et'e
 conjectur'ee par Jean Lannes et le deuxi`eme auteur. La principale
 indication soutenant cette conjecture 'etait un r'esultat combinatoire
 de G. Andrews : la somme altern'ee des s'eries de Poincar'e des
 modules consid'er'ees est nulle.  Ce r'esultat a des cons'equences
 homotopiques et permet de d'emontrer pour ces spectres un r'esultat
 du type de la conjecture de Segal pour les classifiants des 2-groupes
 ab'eliens 'el'ementaires.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Ostvaer/cstar

Title:  Homotopy theory of C*-algebras
Author: Paul Arne Ostvaer
MSC classes: 	46L99; 55P99

Abstract:


     In this work we construct from ground up a homotopy theory of C*-algebras. 
This is achieved in parallel with the development of classical homotopy theory 
by first introducing an unstable model structure and second a stable model structure. 
The theory makes use of a full fledged import of homotopy theoretic techniques into 
the subject of C*-algebras.

     The spaces in C*-homotopy theory are certain hybrids of functors represented by 
C*-algebras and spaces studied in classical homotopy theory. In particular, we employ 
both the topological circle and the C*-algebra circle of complex-valued continuous 
functions on the real numbers which vanish at infinity. By using the inner workings 
of the theory, we may stabilize the spaces by forming spectra and bispectra with 
respect to either one of these circles or their tensor product. These stabilized 
spaces or spectra are the objects of study in stable C*-homotopy theory.
  
     The stable homotopy category of C*-algebras gives rise to invariants such as stable 
homotopy groups and bigraded cohomology and homology theories. We work out examples 
related to the emerging subject of noncommutative motives and zeta functions of C*-algebras. 
In addition, we employ homotopy theory to define a new type of K-theory of C*-algebras. 

     
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