---------------------------
I had to do some hand editing of abstracts this time, so remember to
include author's name and title of paper with the abstract, at the
least.  It is also suggested that you include author's e-mail and AMS
subject classifications.  

7 new papers this time, from Andersen-Bauer-Grodal-Pedersen,
Baas-Dundas-Rognes, Granja, Grojnowski (this is his old paper about
equivariant elliptic cohomology), Hornbostel, Kuhn, and Morava.  

                  Mark Hovey

New papers appearing on hopf between 5/17/03 and 6/18/03

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Andersen-Bauer-Grodal-Pedersen/loopnotlie

Title: A finite loop space not rationally equivalent to a compact Lie group
Authors: Kasper K. S. Andersen, Tilman Bauer, Jesper Grodal, Erik K. Pedersen
Subj-class: Algebraic Topology; Geometric Topology
MSC-class: 55P35; 55P15, 55R35
Comments: 8 pages, arXiv : math.AT/0306234

We construct a connected finite loop space of rank $66$ and dimension
$1254$ whose rational cohomology is not isomorphic as a graded vector
space to the rational cohomology of any compact Lie group, hence
providing a counterexample to a classical conjecture. Aided by machine
calculation we verify that our counterexample is minimal, i.e., that
any finite loop space of rank less than $66$ is in fact rationally
equivalent to a compact Lie group, extending the classical known bound
of $5$.

2.
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 

Addresses of Authors:
Department of Mathematical Sciences
The Norwegian University of Science and Technology
NO-7491 Trondheim
Norway 

Department of Mathematical Sciences
The Norwegian University of Science and Technology
NO-7491 Trondheim
Norway 

Department of Mathematics
University of Oslo
NO-0316 Oslo
Norway

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.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Granja/notehpn

Title: Self maps of HP^n via the unstable Adams spectral sequence
Authors: Gustavo Granja
AMS Classification numbers:  55S35,55S36,55S37

Address of Author:
Departamento de Matematica
Instituto Superior Tecnico
Av. Rovisco Pais
1049-001 Lisboa
Portugal

Email address of Author:
ggranja@math.ist.utl.pt

Abstract: We use obstruction theory based on the unstable Adams spectral
sequence to construct self maps of finite quaternionic projective spaces.
As a result, a conjecture of Feder and Gitler regarding the classification
of self maps up to homology is proved in two new cases.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Grojnowski/deloc

Delocalized equivariant elliptic cohomology
by Ian Grojnowski

This is an old paper, which has been circulating quietly for almost a
decade.

It contains a definition of an equivariant elliptic cohomology theory
for compact connected Lie groups and reasonable topological spaces.
The theory is defined over Q, i.e. neglects torsion completely, and
yet was still interesting.

This is because of the well known heuristic identifying elliptic
cohomology with something like the K-theory of the loop space. The
functor of "loops into" is not local---there is no Mayer-Vietoris
style patching.  Yet elliptic cohomology has such a property.

However the equivariant elliptic cohomology defined here does not
satisfy such a naive locality propery. Instead, the elliptic
cohomology of a space is a non-trivial bundle on the canonical abelian
variety associated to the group.

The crudest invariant of such a bundle is its first Chern class.
This is a combinatorial shadow of the failure of locality.

These same obstruction invariants occur in the study of semi-infinite
D-modules on the infinitesimal neighbourhood of formal loops in the
loop space of an algebraic variety; just as one would expect.

--
Since this paper was written there have been several developments.
Rosu and Ando used this theory to give a new proof of Witten rigidity,
and Greenlees constructed a model for that part of rational
equivariant S^1 homotopy that is seen by an elliptic cohomology
theory.

(There has also been the extraordinary work of Hopkins et al on tmf).

5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Hornbostel/Motchrom

Chromatic motivic homotopy theory
by Jens Hornbostel

We construct a motivic version of the chromatic filtration and the
chromatic spectral sequence.  This should be used to study the stable
${\bf A}^1$-homotopy groups of the motivic sphere spectrum.

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

Title: Localization of Andre--Quillen--Goodwillie towers, and the
periodic homology of infinite loopspaces

Author: Nicholas J. Kuhn      

AMS classification numbers: 55P43, 55P47, 55N20, 18G55                            

Address: Department of Mathematics, University of Virginia, 
Charlottesville, VA 22903    

email: njk4x@virginia.edu

abstract:

Let K(n) be the nth Morava K--theory at a prime p.  This paper is a
thorough study of questions like the following: to what extent does the
K(n)--localization, or the K(n)--homology, of a spectrum X determine the
K(n)--homology of its 0th space X_0?     Our methods combine
techniques from modern homotopical algebra with chromatic homotopy. In
particular, we use the telescopic functors of Bousfield and the author
(dependent on the Nilpotence Theorem of Devanitz, Hopkins, and Smith),
as well as Topological Andre--Quillen Homology and Goodwillie calculus in
nonconnective settings. 

7.
http://hopf.math.purdue.edu/cgi-bin/generate?/Morava/SegalMS

Heisenberg groups and algebraic topology
by Jack Morava
	
This paper overlaps considerably with earlier, sketchier papers 
about the Tate cohomology of circle actions and its connection
to Heisenberg groups. It will appear in the Segal Festschrift:

We study the Madsen-Tillmann spectrum $\C P^\infty_{-1}$ as a quotient 
of the Mahowald pro-object $\C P^{\infty}_{-\infty}$, which is closely 
related to the Tate cohomology of circle actions. That theory has an
associated symplectic structure, whose symmetries define the Virasoro 
operations on the cohomology of moduli space constructed by Kontsevich 
and Witten. 


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