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4 new papers this time, from Blanc, Harper (again, this is John
E. Harper of Notre Dame, not John Harper of Rochester), Kuhn, and 
Sati-Schreiber-Stasheff.  

                  Mark Hovey

New papers appearing on hopf between 1/18/07 and 3/3/08


1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Blanc/quil

Title:      Generalized Andre-Quillen Cohomology
Author:     David Blanc
Address:    Dept. of Mathematics, U. Haifa, Haifa, Israel

Abstract:

   We explain how the approach of Andre and Quillen to defining
cohomology and homology as suitable derived functors extends to
generalized (co)homology theories, and how this identification may be
used to study the relationship between them.

   As a side benefit, we clarify exactly what assumptions on an
(algebraic) category are needed in order for the approach of Beck and
Andre-Quillen to work.

   We also show how the description may be applied to construct
universal coefficient and reverse Adams spectral sequences.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Harper/QuillenHomology

Title: Bar constructions and Quillen homology of modules over operads
Author: John E. Harper
Author's mailing address: Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA

Comments: 33 pages, uses xy-pic; compiled the .tex file without using
the dvips,ps options in xy-pic, to ensure .dvi is device independent,
but diagrams may now appear jagged, etc.

Abstract: This paper shows that Quillen derived homology of modules
and algebras over an operad, for symmetric sequences of symmetric
spectra and unbounded chain complexes, can be calculated using
simplicial bar constructions, modulo cofibrancy conditions. Working
with several model category structures, a homotopical proof is given,
after showing that certain homotopy colimits in modules and algebras
over an operad can be easily understood. The key result here, which is
at the heart of this paper, is showing that the forgetful functor
commutes with certain homotopy colimits.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Kuhn/telescopic

Title: A guide to telescopic functors

Author: Nicholas J. Kuhn

Address: University of Virginia, Charlottesville, VA 22904

Abstract: In the mid 1980's, Pete Bousfield and I constructed certain
p--local `telescopic' functors Phi_n from spaces to spectra, for each
prime p and each positive integer n. These have striking properties
that relate the chromatic approach to homotopy theory to infinite
loopspace theory: roughly put, the spectrum Phi_n(Z) captures the v_n
periodic homotopy of a space Z.

Recently there have been a variety of new uses of these functors,
suggesting that they have a central role to play in calculations of
periodic phenomena.  Here I offer a guide to their construction,
characterization, application, and computation.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Sati-Schreiber-Stasheff/LCon

Title: 
L-infinity algebra connections and applications to String- and Chern-Simons n-transport

Authors: 
Hisham Sati, Urs Schreiber and Jim Stasheff 

Abstract:

We give a generalization of the notion of a Cartan-Ehresmann
connection from Lie algebras to L-infinity -algebras and use it to
study the obstruction theory of lifts through higher String-like
extensions of Lie algebras. We find (generalized) Chern-Simons and
BF-theory functionals this way and describe aspects of their parallel
transport and quantization.

It is known that over a D-brane the Kalb-Ramond background field of
the string restricts to a 2-bundle with connection (a gerbe) which can
be seen as the obstruction to lifting the PU(H)-bundle on the D-brane
to a U(H)-bundle. We discuss how this phenomenon generalizes from the
ordinary central extension U(1) -> U(H) -> PU(H) to higher categorical
central extensions, like the String-extension B U(1) -> String(G) ->
G. Here the obstruction to the lift is a 3-bundle with connection (a
2-gerbe): the Chern-Simons 3-bundle classified by the first Pontrjagin
class.  For G = Spin(n) this obstructs the existence of a
String-structure. We discuss how to describe this obstruction problem
in terms of Lie n-algebras and their corresponding categorified
Cartan-Ehresmann connections. Generalizations even beyond String-
extensions are then straightforward. For G = Spin(n) the next step is
"Fivebrane structures'' whose existence is obstructed by certain
generalized Chern-Simons 7-bundles classified by the second Pontrjagin
class.

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