Subject: new Hopf listings #118 Date: 16 May 2001 15:46:25 -0400 From: Mark Hovey To: dmd1@lehigh.edu The re-organization of Hopf threw me off somewhat, so I might have missed a paper. Let me know if you think I missed yours. Mark Hovey New papers appearing on hopf between 3/5/01 and 5/16/01 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Aguade-Ruiz/mapsBKtoBK Maps between classifying spaces of Kac-Moody groups by Jaume Aguad\'e and Albert Ru\'iz (aguade@mat.uab.es, cirera@mat.uab.es) Kac-Moody groups are an important generalisation of Lie groups. Roughly speaking, they are like "Lie groups with infinite Weyl groups". Let K be the unitary form of a Kac-Moody group of rank two. In this paper we determine the self maps of BK. Contents: 1. Introduction. 2. Rank two Kac-Moody groups. 3. Relations between global and local maps. 4. Maps into BK^p and representations. 5. Admissible matrices. 6. Groups with the same classifying space. 7. Adams maps. 8. Homotopically trivial self maps. 9. Detecting maps on the maximal torus. 10. [BK,BK]. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Costenoble-May-Waner/CMWfinal Equivariant orientation theory by S.R. Costenoble, J.P. May, and S. Waner subjclass: Primary 55P91; Secondary 18B40, 20L15, 55N25, 55N91, 55P20, 55R91, 57Q91, 57R91 Hofstra University, University of Chicago, and Hofstra University Steven.R.Costenoble@Hofstra.edu, may@uchicago.edu, matszw@hofstra.edu We give a long overdue theory of orientations of G-vector bundles, topological G-bundles, and spherical G-fibrations, where G is a compact Lie group. The notion of equivariant orientability is clear and unambiguous, but it is surprisingly difficult to obtain a satisfactory notion of an equivariant orientation such that every orientable G-vector bundle admits an orientation. Our focus here is on the geometric and homotopical aspects, rather than the cohomological aspects, of orientation theory. Orientations are described in terms of functors defined on equivariant fundamental groupoids of base G-spaces, and the essence of the theory is to construct an appropriate universal target category of G-vector bundles over orbit spaces G/H. The theory requires new categorical concepts and constructions that should be of interest in other subjects where analogous structures arise. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Notbohm/bdi4 (This is a new version of an paper previously announced). 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 $BDI(4)$. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Notbohm/orthogonal (This is a new version of a paper previously announced). 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 \pcg s. 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. ---------------------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 (Netscape< Internet Explorer) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to 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.