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6 new papers this time, from Baas-Dundas-Rognes (an update), Richter,
Sinha, Strickland, and (Jim) Turner (2),  

                  Mark Hovey

New papers appearing on hopf between 6/18/03 and 7/11/03

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Baas-Dundas-Rognes/segal60

Title of Paper: Two-vector bundles and forms of elliptic cohomology
Authors: Nils A. Baas, Bjorn I. Dundas and John Rognes 
Email address of Authors:
baas@math.ntnu.no, dundas@math.ntnu.no and rognes@math.uio.no

In this paper we define 2-vector bundles as suitable bundles of 2-vector
spaces over a base space, and compare the resulting 2-K-theory with
the algebraic K-theory spectrum K(V) of the 2-category of 2-vector
spaces, as well as the algebraic K-theory spectrum K(ku) of the
connective topological K-theory spectrum ku.  We explain how K(ku)
detects v_2-periodic phenomena in stable homotopy theory, and as such
is a form of elliptic cohomology.

(This is an new version of a paper previously on Hopf). 

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Richter/Richter-Lambda-EHP

Title: Lambda algebra unstable composition products and the 
       Lambda EHP sequence

Author: William Richter

AMS Classification numbers: 55T15, 55Q40, 55Q25
Address: Math Department, Northwestern University, Evanston IL 6020 
Email: richter@math.nwu.edu
Abstract:

Simple combinatorial proofs are given of Lambda algebra results,
mostly due to Priddy & the 6 authors, but also the ``Adams filtration
better'' unstable Lambda products of Wang, Mahowald and Singer:

Lambda^{s,t}(n) @ Lambda(n+t ) ---> Lambda(n)

which imply the folklore Lambda EHP sequence

Lambda(n)  >-E--> Lambda(n+1) -H-->> Lambda(2n+1) 

The 6 authors proved Lambda(n) is a chain complex, but not that H is a
chain map.  A careful reader could deduce a proof from the papers of
Wang, Mahowald and Singer, but Singer, who best stated the formulas,
gave no proofs.  New results: combinatorial proofs of the Lambda
admissible monomial basis; the differential d is well-defined.

The paper should be accessible to geometers interested in forthcoming
applications with Mahowald on 3-cell Poincare complexes.  Perhaps the
Lambda algebra is undergoing a Renaissance, as 2 young people, Mark
Behrens and Mizuho Hikida are doing interesting new work in it.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Sinha/compactify

Title: Manifold theoretic compactifications of configuration spaces.
Author: Dev P. Sinha
AMS Class: 55R80; 32J05 
LANL ID: math.GT/0306385
Addresses: Departments of Mathematics, University of Oregoni, Eugene, OR 97403
Email: dps@math.uoregon.edu 

Abstract:
We present new definitions for and give a comprehensive treatment  of the
canonical compactification of configuration spaces due to  Fulton-MacPherson
and  Axelrod-Singer in the setting of smooth manifolds, as well as a
simplicial variant of this compactification.  Our constructions are
elementary and give simple global coordinates for the compactified
configuration space of a general manifold embedded in Euclidean space.   We
stratify the canonical compactification, identifying the 
diffeomorphism types of the strata in terms of spaces of  configurations in
the tangent bundle, and give completely explicit local coordinates  around
the strata as needed to define a manifold with corners.    
We analyze the quotient map from the canonical to the
simplicial  compactification, showing it is a homotopy equivalence.  We
define projection maps and diagonal maps, which for the simplicial variant
satisfy cosimplicial identities.  

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Strickland/axsurv

Axiomatic stable homotopy--a survey

by N. P. Strickland

We survey various approaches to axiomatic stable homotopy theory,
with examples including derived categories, categories of
(possibly equivariant or localized) spectra, and stable categories of
modular representations of finite groups.  We focus mainly on
representability theorems, localisation, Bousfield classes, and
nilpotence.

5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Turner/finite

On simplicial commutative algebras with finite Andre-Quillen homology

by James M. Turner

L. Avramov, following D. Quillen, posed a conjecture to the effect that
if $R \to A$ is a homomorphism of Noetherian rings then the
Andr\'e-Quillen homology on the category of A-modules satisfies:
$D_{s}(A|R;-) = 0$ for $s\gg 0$ implies $D_{s}(A|R;-) = 0$ for s>2. In
an earlier paper, the author posed an extended version of this
conjecture which considered A to be a simplicial commutative R-algebra
with Noetherian homotopy such that the characteristic of $\pi_{0}A$ is
non-zero. In addition, a homotopy characterization of such algebras was
described. The main goal of this paper is to develop a strategy for
establishing this extended conjecture and provide a complete proof when
R is Cohen-Macaulay of characteristic 2.  Note: this paper replaces
"Nilpotency in the homotopy of simplicial commutative algebras".

6.
http://hopf.math.purdue.edu/cgi-bin/generate?/Turner/Gorenstein

Characterizing Simplicial Commutative Algebras with Vanishing
Andr'e-Quillen Homology

by James M. Turner

The use of homological and homotopical devices, such as Tor
and Andr\'e-Quillen homology, have found substantial use in
characterizing commutative algebras. The primary category setting has
been differentially graded algebras and modules, but recently
simplicial categories have also proved to be useful settings. In this
paper, we take this point of view up a notch by extending some recent
uses of homological algebra in characterizing Noetherian commutative
algebras to characterizing simplicial commutative algebras having
finite Noetherian homotopy through the use of simplicial homotopy
theory. These characterizations involve extending the notions
of locally complete intersections and locally Gorenstein algebras to
the simplicial homotopy setting.


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