4 new papers this month, from Devinatz, Dugger, IsaksenD, and Sinha.  

                  Mark Hovey

New papers appearing on hopf between 8/7/04 and 9/2/04

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Devinatz/recog


Title:   Recognizing Hopf algebroids defined by a group action
Author:  Ethan Devinatz
e-mail:  devinatz@math.washington.edu

Abstract:  Let A be a complete noetherian regular local ring, and suppose
that S is a profinite group acting continuously on A via ring homomorphisms.
Let T be the algebra of continuous functions from S to A.  Then (A,T)
has a canonical structure of a complete Hopf algebroid, determined by the
action of S on A.  We give necessary and sufficient conditions for a general 
Hopf algebroid to be of this form.  Applications to Morava theory are also
discussed.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Dugger/milnor

Title: Notes on the Milnor conjectures

Author: Daniel Dugger

email: ddugger@math.uoregon.edu

Abstract: 

These are some expository notes on the two Milnor conjectures and
their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/IsaksenD/gencohlgy

Title: Generalized cohomology of pro-spectra

Author: Daniel C. Isaksen

E-mail: isaksen@math.wayne.edu

AMS classification: 55T25, 55P42, 55U35, 55N20, 18G55 (Primary), 
  19L99 (Secondary)

Abstract:

We present a closed model structure for the category of pro-spectra
in which the weak equivalences are detected by stable homotopy pro-groups.
With some bounded-below assumptions, weak equivalences are also detected
by cohomology as in the classical Whitehead theorem for spectra.
We establish an Atiyah-Hirzebruch spectral sequence in this context,
which makes possible the computation of topological K-theory 
(and other generalized cohomology theories) of pro-spectra.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Sinha/opknot

Title: Operads and knot spaces
Author: Dev Sinha
E-mail: dps@math.uoregon.edu

Abstract: Let F_m be the space of knotted intervals in I^m equipped with a
trivialization through immersions.  We show that the totalization
of the Kontsevich operad provides a model for the embedding calculus
tower for F_m.  Combined with results of Goodwillie-Klein-Weiss
and Volic, this resolves Kontsevich's conjecture of existence of such
a model which captures the homotopy type of F_m when m>3 and which
classifies finite-type framed knot invariants when m=3.  

We carefully develop the Kontsevich operad, which is closely related
to the Fulton-MacPherson operad and weakly equivalent to the little
cubes operad.  In doing so we show that the standard simplicial model
for the two-sphere carries an operad structure in the opposite category
of pointed sets.  We apply the well-developed machinery of McClure and 
Smith on operads with multiplication to deduce that our model has a 
little two-cubes action.  

(Note: if you want the dvi file to contain the figures, you need to
download the directory Figures as well.  The pdf file already has the
figures built in.)


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