Subject: new Hopf listings
From: Mark Hovey
Date: 05 Sep 2005 08:55:45 -0400
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
Author's e-mail address: bergnerj@member.ams.org
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
Author's e-mail address: bergnerj@member.ams.org
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
Email address: schebolu@uwo.ca
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
e-mail: jens.hornbostel@mathematik.uni-regensburg.de,
niko.naumann@mathematik.uni-regensburg.de
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
Email address of Authors:
lueck@math.uni-muensetr.de
reichh@math.uni-muenster.de
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
Email address: dn8@mcs.le.ac.uk
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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