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There are 6 new papers this time, from Bergner (2), Chebolu,
Hornbostel-Naumann, Lueck-Reich, and Notbohm.  
                  Mark Hovey

New papers appearing on hopf between 8/4/05 and 9/5/05

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bergner/MultiSort

Title: Rigidification of algebras over multi-sorted algebraic
theories

Author: Julia E. Bergner

AMS Classification: 18C10, 18G30, 18E35, 55P48

arXiv submission number: math.AT/0508152

Author's address:
Kansas State University
138 Cardwell Hall
Manhattan, KS 66506

Abstract: We define the notion of a multi-sorted algebraic theory,
which is a generalization of an algebraic theory in which the
objects are of different ``sorts." We prove a rigidification
result for simplicial algebras over these theories, showing that
there is a Quillen equivalence between a model category structure
on the category of strict algebras over a multi-sorted theory and
an appropriate model category structure on the category of
functors from a multi-sorted theory to the category of simplicial
sets. In the latter model structure, the fibrant objects are
homotopy algebras over that theory.  Our two main examples of
strict algebras are operads in the category of simplicial sets and
simplicial categories with a given set of objects.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bergner/SimplicialMonoids

Title: Simplicial monoids and Segal categories

Author: Julia E. Bergner

AMS Classification: 18G30, 18E35, 18C10, 55U40

arXiv submission number: math.AT/0508416

Author's address: Kansas State University 138 Cardwell Hall
Manhattan, KS 66506

Abstract: Much research has been done on structures equivalent to
topological or simplicial groups.  In this paper, we consider
instead simplicial monoids.  In particular, we show that the usual
model category structure on the category of simplicial monoids is
Quillen equivalent to an appropriate model category structure on
the category of simplicial spaces with a single point in degree
zero.  In this second model structure, the fibrant objects are
reduced Segal categories. We then generalize the proof to relate
simplicial categories with a fixed object set to Segal categories
with the same fixed set in degree zero.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Chebolu/chromatic

Title: Refining thick subcategory theorems
Author: Sunil Chebolu
AMS classification numbers: Primary: 55P42, 18G55, 19A99
Address: Department of Mathematics, University of Western Ontario,
London, ON, N6A 5B7 
Abstract: 
We use a $K$-theory recipe of Thomason to obtain classifications of
triangulated subcategories via refining some standard thick subcategory
theorems. We apply this recipe to the full subcategories of finite
objects in the derived categories of rings and the stable homotopy
category of spectra. This gives, in the derived categories, a complete
classification of the triangulated subcategories of perfect complexes
over some noetherian rings. In the homotopy category of spectra we
obtain only a partial classification of the triangulated subcategories
of the finite $p$-local spectra. We use this partial classification to
study the lattice of triangulated subcategories.  This study gives some
new evidence to a conjecture of Adams that the thick subcategory $\C_2$
can be generated by iterated cofiberings of the Smith-Toda complex.  We
also discuss various consequences of these classifications theorems.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Hornbostel-Naumann/f-invofbeta

Title: Beta-elements and divided congruences
Authors: Jens Hornbostel, Niko Naumann

Abstract: The f-invariant is an injective homomorphism from the 2-line
of the Adams-Novikov spectral sequence to a group which is closely
related to divided congruences of elliptic modular forms. We compute the
f-invariant for two infinite families of beta-elements and explain the
relation of the arithmetic of divided congruences with the Kervaire
invariant one problem.

5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Lueck-Reich/lueck+reich0805

Title of Paper: Detecting K-theory by cyclic homology

Author(s): Wolfgang Lueck and Holger Reich

AMS Classification number: 19D55

xxx_archive: math.KT/0509002

Addresses of Authors:

Mathematisches Institut 
Westfaelische Wilhelms-Universitaet
Einsteinstr. 62
48149 Muenster
Germany

Text of Abstract (try for 20 lines or less) 

We discuss which part of the rationalized algebraic K-theory 
of a group ring is detected via trace maps to Hochschild homology, 
cyclic homology, periodic cyclic or negative cyclic homology.

6.
http://hopf.math.purdue.edu/cgi-bin/generate?/Notbohm/cmcomplex

Title: Cohen-Macaulay and Gorenstein complexes from a topological 
       point of view
       
Author: Dietrich Notbohm

AMS Classification numbers: 13F55, 55R35

Address of Author: Dept. of Mathematics, University of Leicester, 
                   University Road, Leicester LE1 7RH, England
                   
Abstract:
The main invariant to study the combinatorics of a simplicial complex
$K$ is the associated face ring or Stanley-Reisner algebra.  Reisner
respectively Stanley explained in which sense Cohen-Macaulay and
Gorenstein properties of the face ring are reflected by geometric and/or
combinatoric properties of the simplicial complex. We give a new proof
for these result by homotopy theoretic methods and constructions.  Our
approach is based on ideas used very successfully in the analysis of the
homotopy theory of classifying spaces.


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