Subject: [dmd1@lehigh.edu (DONALD M. DAVIS)] new Hopf listings From: Mark Hovey Date: 25 Mar 1998 13:06:33 +0000 -------------- Two new papers this time. Mark Hovey New papers uploaded to Hopf between 3/19/98 and 3/25/98: 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/DavisD-Zelov/vitaly Some embeddings and nonimmersions of real projective spaces Donald M. Davis and Vitaly Zelov submitted to Boardman conference proceedings Abstract We prove the following new results. If alpha(n)=2, then RP^{16n+8} cannot be immersed in R^{32n+3}, and RP^{16n+10} cannot be immersed in R^{32n+11}. If alpha(n)>2, then RP^{8n+4} can be immersed in R^{16n+1}. The method is obstruction theory. The main novelty is careful consideration of secondary indeterminacy for the nonimmersions, and a combining of two methods for the embeddings. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/WuJ/newsimplicialgroup_1 On Combinatorial Descriptions of Homotopy Groups of Certain Spaces This is the revised version of the paper title "On Combinatorial Descriptions of Homotopy Groups of K(ss; 1)" on the archive. It is significantly changed from the version which has been on the archive, including adding some new results. Jie Wu Department of Mathematics University of Pennsylvania Philadelphia, PA 19104 USA jiewu@math.upenn.edu Included file: newsimplicialgroup_1.dvi Abstract: 1) We give combinatorial groups which occur naturally for which the homotopy groups of the suspension of $K(\pi,1)$ for general $\pi$ are the centers. [Theorem 1.5]. 2) We give explicit groups which occur naturally for which all of the homotopy groups of the 3-sphere are the centers [Theorem 1.2]. 3) Furthermore we give an explicit finitely presented nilpotent group for which the (general) higher homotopy group of the 3-sphere is the torsion of the center [Proposition 4.9]. In other words, there are explicit finite 2-complexes of which the (general) higher homotopy groups of the $3$-sphere are the torsion of the centers of the fundamental groups. 4) Our descriptions are NOT yet calculations of higher homotopy groups. But it is expected to have uses of computer for studying the centers of these combinatorial groups. 5) We have a group theoretical description of the torsion of homotopy groups of any simply connected space [Theorem 2.22]. We do not yet have an explicit combinatorial description of homotopy groups of higher spheres. 6) Our description allows us to compute the homotopy groups of Cohen's construction of the 1-sphere (the space that is considerable useful in mathematical physics and deformation theory) and to reprove Milnor's unpublished example on Moore's problem. ---------------------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 -------