Subject: new Hopf listings From: Mark Hovey Date: 29 Jun 1998 02:33:59 -0400 We have two new papers this time and one final version. There is also a new picture, taken at the Adams Symposium in 1990, at http://hopf.math.purdue.edu/pub/new-html/contribpics.html There is a link to this page from the main hopf page. Mark Hovey New papers uploaded to hopf between 6/17/98 and 6/29/98: 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Arone-Mahowald/ArMahowald The Goodwillie Tower of the identity functor and the unstable periodic homotopy of spheres AMS Classification: 55P47, 55Q40, 55S12 Greg Arone arone@math.uchicago.edu Mark Mahowald mark@math.nwu.edu We investigate Goodwillie's ``Taylor tower'' of the identity functor from spaces to spaces. More specifically, we reformulate Johnson's description of the Goodwillie derivatives of the identity, and prove that when evaluated at an odd-dimensional sphere, the only layers in the tower that are not contractible are those indexed by a prime power. Furthermore, in the case of a sphere the tower is finite in $v_k$-pe- riodic homotopy. It has $k+1$ stages if the sphere is odd dimensional, and $2(k+1)$ stages if the sphere is even-dimensional. This is a revised version of a previously uploaded preprint. The paper has been accepted for publication, and is now in its final form. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Moller/toricrep Title: Toric representations of p-compact groups. Author: J.M. M{\o}ller Department of Mathematics University of Copenhagen DK-2100 Copenhagen Denmark AMS Classification numbers: 55R35, 55S37 Address of author: Department of Mathematics University of Copenhagen DK-2100 Copenhagen Denmark e-mail: moller@math.ku.dk Abstract: We compute the mapping spaces map(X,Y) where (X,Y)=(BSU(3),BF_4), (BG_2,BF_4), and (BSU(3),BG_2). 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Sinha/mugcomps Computations in Complex Equivariant Bordism Theory by Dev Sinha Mathematics Department Box 1917 Brown University Providence, RI 02912 E-mail: dps@math.brown.edu In this paper we present computations of the ring structure of the coefficients of equivariant bordism, answering questions which have been open since these theories were first defined by Conner and Floyd and tom Dieck. We have a result which establishes an algebraic framework in which to understand equivariant bordism for any group such that any proper subgroup is contained in a proper normal subgroup. This class of groups includes abelain groups and $p$-groups. Our general result is computationally satisfying when one can find a suitable representation of $MU^G_*$. For abelian groups the map to completion at the augmentation ideal seems to be such a representation, so we make explicit computations of that map. We give applications to the geometry of lens spaces and $S^1$ actions on stably complex four-manifolds. ---------------------Instructions----------------------------- To subscribe or unsubscribe to this list, send a message to Don Davis at dmd1@lehigh.edu with your e-mail address and name. Please make sure he is using the correct e-mail address for you. To see past issues of this mailing list, point your WWW browser to http://www.cs.wesleyan.edu/Math/Guests/Mark If this doesn't work or is missing a few issues, try http://www.lehigh.edu/~dmd1/public/www-data/algtop.html , which also has the other messages sent to Don's list. To get the papers listed above, point your WWW client (Mosaic, Netscape) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to conference announcements, Purdue seminars, and other math related things on this page as well. The general xxx archive URL is http://xxx.lanl.gov. More useful is the front end developed by Greg Kuperberg: http://front.math.ucdavis.edu You can also use ftp to hopf.math.purdue.edu, and login as ftp. Then cd to pub. Files are organized by author name, so papers by me are in pub/Hovey. If you want to download a file using ftp, you must type binary before you type get . To put a paper of yours on the archive, cd to /pub/incoming. Transfer the dvi file using binary, by first typing binary then put You should also transfer an abstract as well. Clarence has explicit instructions for the form of this abstract: see http://hopf.math.purdue.edu/pub/submissions.html. In particular, your abstract is meant to be read by humans, so should be as readable as possible. I reserve the right to edit unreadable abstracts. You should then e-mail Clarence at wilker@math.purdue.edu telling him what you have uploaded. For instructions on uploading papers to xxx, see http://front.math.ucdavis.edu I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive. ------- End of forwarded message ------- ------- End of forwarded message -------