Subject: new Hopf listings From: Mark Hovey Date: 25 Jan 2000 15:26:10 -0500 7 new papers this time. Mark Hovey New papers uploaded to hopf between 1/2/00 and 1/25/00. 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Anderson-DavisJ/MacPherson Title: Mod 2 Cohomology of Combinatorial Grassmannians Authors: Laura Anderson and James F. Davis Abstract: Matroid bundles, introduced by MacPherson, are combinatorial analogues of real vector bundles. This paper sets up the foundations of matroid bundles, and defines a natural transformation from isomorphism classes of real vector bundles to isomorphism classes of matroid bundles, as well as a transformation from matroid bundles to spherical quasifibrations. The poset of oriented matroids of a fixed rank classifies matroid bundles, and the above transformations give a splitting from topology to combinatorics back to topology. This shows the mod 2 cohomology of the poset of rank k oriented matroids (this poset classifies matroid bundles) contains the free polynomial ring on the first k Stiefel-Whitney classes. The homotopy groups of this poset are related to the image of the J-homomorphism from stable homotopy theory. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Dwyer-Wilkerson/center-calc/ce nter-calc Centers and Coxeter elements by W. G. Dwyer and C. W. Wilkerson dwyer.1@nd.edu wilker@math.purdue.edu Abstract: Suppose that $G$ is a connected compact Lie group. We show that simple numerical information about the Weyl group of $G$ can be used to obtain bounds, often sharp, on the size of the center of $G$. These bounds are obtained with the help of certain Coxeter elements in the Weyl group. Variants of the method use generalized Coxeter elements and apply to $p$-compact groups; in this case a splitting theorem emerges. The Lie group results are mostly known, but our arguments have a conceptual appeal. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Hovey-Palmieri/quillen Stably thick subcategories of modules over Hopf algebras by Mark Hovey and John Palmieri hovey@member.ams.org and palmieri@member.ams.org We discuss a general method for classifying certain subcategories of the category of finite-dimensional modules over a finite-dimensional cocommutative Hopf algebra B. Our method is based on that of Benson-Carlson-Rickard, who classify such subcategories when B=kG, the group ring of a finite group G over an algebraically closed field k. We get a similar classification when B is a finite sub-Hopf algebra of the mod 2 Steenrod algebra, with scalars extended to the algebraic closure of Z/2. Along the way, we prove a Quillen stratification theorem for cohomological varieties of modules over any B, in terms of quasi-elementary sub-Hopf algebras of B. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Notbohm/bdi4 ON THE 2-COMPACT GROUP DI(4) Author: D. Notbohm Besides the simple connected compact Lie groups there exists one further simple connected 2-compact group, constructed by Dwyer and Wilkerson, the group $DI(4)$. The mod-2 cohomology of the associated classifying space $BDI(4)$ realizes the rank 4 mod-2 Dickson invariants. We show that mod-2 cohomology determines the homotopy type of the space $BDI(4)$ and that the maximal torus normalizer determines the isomorphism type of $DI(4)$ as 2-compact group. We also calculate the set of homotopy classes of self maps of $BDI(4)$. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Notbohm/orthogonal A UNIQUENESS RESULT FOR ORTHOGONAL GROUPS AS 2-COMPACT GROUPS D. Notbohm Two connected compact Lie groups are isomorphic if and only if their maximal torus normalizer are isomorphic. It is conjectured that this result generalizes to p-compact groups. Here, we prove the generalization for orthogonal groups $O(n)$, the special orthogonal groups $SO(2k+1)$ and the spinor groups $Spin(2k+1)$ considered as 2-compact groups. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/SchwartzL/FK Author: Lionel Schwartz Title: La filtration de Krull de la categorie U et la cohomologie des espaces Jan. 6, 2000 The present paper gives a proof of a conjecture of N. Kuhn : if the mod 2 cohomology of a space has finite Krull filtration in the category of unstable modules, it has to be a locally finite unstable module. Some technical assumptions are required. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/WuJ/newwgroup Title of Paper: A braided simplicial group Author(s): Jie Wu Email address of Authors: matwuj@nus.edu.sg Text of Abstract: By studying braid group actions on Milnor's construction of the 1-sphere, we show that the general homotopy group of the 3-sphere is the fixed set of the pure braid group action on a certain combinatorially described group. We also give a certain representation of higher differentials in the Adams spectral sequence for the homotopy groups of the 2-sphere. Comments are welcome. ---------------------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.math.wesleyan.edu/~mhovey/archive/ If this doesn't work or is missing a few issues, try http://www.lehigh.edu/~dmd1/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 largest archive of math preprints is at http://xxx.lanl.gov There is an algebraic topology section in this archive. The most useful way to browse it or submit papers to it is via the front end developed by Greg Kuperberg: http://front.math.ucdavis.edu To get the announcements of new papers in the algebraic topology section at xxx, send e-mail to math@xxx.lanl.gov with subject line "subscribe" (without quotes), and with the body of the message "add AT" (without quotes). You can also access Hopf through ftp. 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/new-html/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. I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive.