Subject: Hopf listings Dec. 2001 Date: 12 Dec 2001 11:43:37 -0500 From: Mark Hovey To: dmd1@lehigh.edu 5 new papers this time. There is also a corrected version of the paper I announced last time on the Lusternik-Schnirelmann category of Sp(3), by Fernandez-Suarez, Gomez-Tato, Strom, and Tanre. Mark Hovey New papers appearing on hopf between 11/13/01 and 12/12/01 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Dugger-Isaksen/hypercover Hypercovers in topology Daniel Dugger, Daniel C. Isaksen 55U35, 14F20, 14F42 Department of Mathematics Purdue University West Lafayette, IN 47907 Department of Mathematics University of Notre Dame Notre Dame, IN 46556 ddugger@math.purdue.edu isaksen.1@nd.edu We show that if U is a hypercover of a topological space X then the natural map from hocolim U to X is a weak equivalence. This fact is used to construct topological realization functors for the A^1-homotopy theory of schemes over real and complex fields. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Scannell-Sinha/knotss A one-dimensional embedding complex by Kevin P. Scannell and Dev P. Sinha St. Louis University and Brown University scannell@slu.edu dps@math.brown.edu We give the first explicit computations of rational homotopy groups of spaces of "long knots" in Euclidean spaces. We define a spectral sequence which converges to these rational homotopy groups whose E^1 term is defined in terms of Lie algebras related to braid groups. For odd k we establish a vanishing line for this spectral sequence, show the Euler characteristic of the rows of this E^1 term is zero, and make calculations of E^2 in a finite range. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Sinha/localcohom The geometry of the local cohomology filtration in equivariant bordism by Dev P. Sinha Brown University dps@math.brown.edu Local cohomology techniques in equivariant homotopy theory, introduced by John Greenlees, may be applied to understand homology of classifying spaces through other equivariant data. In this paper we relate the local cohomology filtration to the families filtration. By doing so, we may identify geometry codified by the local cohomology filtration in the setting of equivariant bordism. The constructions which arise are naturally analyzed by localized K-theory machinery due to Atiyah and Segal, which we review. This paper has appeared in Homology, Homotopy and Applications. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/WuJ/coHspacewu On co-H maps to the suspension of the projective plane by Jie Wu Department of Mathematics National University of Singapore Singapore 117543 Republic of Singapore matwuj@nus.edu.sg We study co-H-maps from a suspension to the suspension of the projective plane and provide examples of non-suspension 3-cell co-H-spaces. These (infinitely many) examples are related to the homotopy groups of the 3-sphere. For each element of order 2 in $\pi_n(S^3)$, there is a corresponding non-suspension co-H-space of cells in dimensions 2, 3 and n+2. Our ideas are to study Hopf invariants in combinatorial way by using the Cohen groups. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/WuJ/mod2Moore2-2 Homotopy Theory of the suspensions of the projective plane by Jie Wu Department of Mathematics National University of Singapore Singapore 117543 Republic of Singapore matwuj@nus.edu.sg The homotopy theory of the suspensions of the real projective plane is largely investigated. The homotopy groups are computed up to certain range. The decompositions of the self smashes and the loop spaces are studied with some applications to the Stiefel manifolds. This paper is essentially from my Ph. D. thesis at Rochester under the supervise of Fred Cohen, and my joint works with Fred Cohen and Paul Selick. The group representation theory, particularly the modular representation theory of symmetric groups, is used much in this article. The table of the homotopy groups computed in this article have been announced without proofs in Cohen's paper in the Handbook of Algebraic Topology by James. ---------------------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 or 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/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.