-----------------------------------------
4 new papers this time, from Bartels-Reich, Goodwillie (Calc III!),
Gorbounov-Malikov, and Kuhn.

                  Mark Hovey

New papers appearing on hopf between 7/11/03 and 8/21/03

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Bartels-Reich/isoIIhopf

Title: On the Farrell-Jones Conjecture for higher algebraic K-theory
Authors: Arthur Bartels, Holger Reich
e-mail adresses: bartelsa@math.uni-muenster.de, reichh@math.uni-muenster.de
arxiv: math.AT/0308030


Abstract:
We prove the Farrell-Jones Isomorphism Conjecture about the algebraic
K-theory of a group ring RG in the case where the group G is the
fundamental group of a closed Riemannian manifold with strictly negative
sectional curvature. The coefficient ring R is an arbitrary associative
ring with unit and the result applies to all dimensions.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Goodwillie/calculus3

Title: Calculus III, Taylor series
Author: Thomas G. Goodwillie
Author's e-mail address: tomg@math.brown.edu

Abstract: We study functors from spaces to spaces or spectra that
preserve weak homotopy equivalences. For each such functor we construct
a universal n-excisive approximation, which may be thought of as its
n-excisive part. Homogeneous functors, meaning n-excisive functors with
trivial (n-1)-excisive part, can be classified: they correspond to
symmetric functors of n variables that are 1-excisive in each
variable. We discuss some important examples, including the identity
functor and Waldhausen's algebraic K-theory.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Gorbounov-Malikov/LG-CY-try

Vertex algebras and the Landau-Ginzburg/Calabi-Yau correspondence
Vassily Gorbounov and Fyodor Malikov

We construct a spectral sequence that converges to the cohomology of the
chiral de Rham complex over a Calabi-Yau hypersurface and whose first
term is a vertex algebra closely related to the Landau-Ginburg
orbifold.  As an application, we prove an explicit orbifold formula for
the elliptic genus of Calabi-Yau hypersurfaces.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Kuhn/Tate

Title: Tate cohomology and periodic localization of polynomial functors
Author: Nicholas J. Kuhn      

AMS classification numbers: Primary 55P65; Secondary 55N22, 55P60, 55P91 
Address: Department of Mathematics, University of Virginia,
Charlottesville, VA 22903   

email: njk4x@virginia.edu

abstract: 
In this paper, we show that Goodwillie calculus, as applied to functors
from stable homotopy to itself, interacts in striking ways with
chromatic aspects of the stable category.  Localized at a fixed prime p,
let T(n) be the telescope of a v_n self map of a finite S--module of
type n.  The Periodicity Theorem of Hopkins and Smith implies that the
Bousfield localization functor associated to T(n) is independent of
choices.  Goodwillie's general theory says that to any homotopy functor
F from S--modules to S--modules, there is an associated tower under F,
{P_dF}, such that F --> P_dF is the universal arrow to a d--excisive
functor.  Our first theorem says that P_dF --> P_{d-1}F always admits a
homotopy section after localization with respect to T(n) (and so also
after localization with respect to Morava K--theory K(n)). Thus, after
periodic localization, polynomial functors split as the product of their
homogeneous factors.  This theorem follows from our second theorem which
is equivalent to the following: for any finite group G, the Tate spectrum
t_G(T(n)) is weakly contractible.  This strengthens and extends previous
theorems of Greenlees--Sadofsky, Hovey--Sadofsky, and Mahowald--Shick.
The Periodicity Theorem is used in an essential way in our proof.  The
connection between the two theorems is via a reformulation of a result
of McCarthy on dual calculus.

 -------------