Subject: new Hopf listings Date: 13 May 2003 07:36:00 -0400 From: Mark Hovey Reply-To: mhovey@wesleyan.edu To: dmd1@lehigh.edu 4 new papers this time, from BrownR, DavisD, Dwyer, and Gottlieb. Mark Hovey New papers appearing on hopf between 4/09/03 and 5/13/03 1. http://hopf.math.purdue.edu/cgi-bin/generate?/BrownR/noncommut-at Title: Towards non commutative algebraic topology Author: Ronald Brown AMS Classification numbers: 55D15, 55U40, 18D35 Address of Author: Mathematics Division, School of Informatics, University of Wales, Bangor, Gwynedd LL57 1UT, UK. Email address of Author: r.brown@bangor.ac.uk Text of Abstract: These are the transparencies (slightly edited) for a seminar at University College, London, on May 7, 2003. They give a quick overview of some background and some directions taken for algebraic methods for higher dimensional, non commutative, local to global problems, including some algebraic models of homotopy types. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/DavisD/E7E8 Representation types and 2-primary homotopy groups of certain compact Lie groups Donald M. Davis 55Q52, 55T15, 57T20 Department of Mathematics Lehigh University Bethlehem, PA 18015 dmd1@lehigh.edu Abstract: Bousfield has shown how the 2-primary v1-periodic homotopy groups of certain compact Lie groups can be obtained from their representation ring with its decomposition into types and its exterior power operations. He has formulated a Technical Condition which must be satisfied in order that he can prove his description is valid. We prove that a simply-connected compact simple Lie group satisfies his Technical Condition if and only if it is not E6 or Spin(4k+2) with k not a 2-power. We then use his description to give an explicit determination of the 2-primary v1-periodic homotopy groups of E7 and E8. This completes a program, suggested to the author by Mimura in 1989, of computing the v1-periodic homotopy groups of all compact simple Lie groups at all primes. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Dwyer/local Localization W. G. Dwyer This is a largely expository paper, which describes the concept of localization, as it usually comes up in topology, and gives some examples of it. The examples include local homology and cohomology, homological localizations of spaces and spectra, and localization with respect to a map f. For appropriate choices of the map f, this last gives constructions related to the Goodwillie calculus and to motivic homotopy theory. There's also a proof that if a localization functor exists, the higher order categorical invariants associated to inverting the local equivalences are trivial. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Gottlieb/eigbndl EIGENBUNDLES, QUATERNIONS, AND BERRY'S PHASE Daniel Henry Gottlieb Given a parameterized space of square matrices, the associated set of eigenvectors forms some kind of a structure over the parameter space. When is that structure a vector bundle? When is there a vector field of eigenvectors? We answer those questions in terms of three obstructions, using a Homotopy Theory approach. We illustrate our obstructions with five examples. One of those examples gives rise to a 4 by 4 matrix representation of the Complex Quaternions. This representation shows the relationship of the Biquaternions with low dimensional Lie groups and algebras, Electro-magnetism, and Relativity Theory. The eigenstructure of this representation is very interesting, and our choice of notation produces important mathematical expressions found in those fields and in Quantum Mechanics. In particular, we show that the Doppler shift factor is analogous to Berry's Phase. ---------------------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://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 Web browser to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There is a web form for submitting papers to Hopf on this site as well. You can also use ftp, explained below. 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, go to http://hopf.math.purdue.edu and use the web form. You can also use anonymous ftp as above. First 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/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.