Subject: new Hopf listings From: Mark Hovey Date: 02 Oct 2000 13:13:11 -0400 Four new papers this time, all from some energetic guy named Greenlees. He maintains a bibliography on Hopf as well, under http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees/greenleesbiblio Mark Hovey New papers appearing on hopf between 9/28/00 and 10/2/00. 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees/axiomatic Title: ``Tate cohomology in axiomatic stable homotopy theory.'' Author: J.P.C.Greenlees AMS classification numbers: 55U35, 55T99, 55P42, 55P91, 55N91 Address: University of Sheffield, UK Email: j.greenlees@shef.ac.uk Abstract: Any smashing localization in an axiomatic stable homotopy theory in the sense of Hovey-Palmieri-Strickland gives rise to a Tate theory. Various known versions of Tate cohomology (for example in commutative algebra, in the cohomology of groups, in equivariant homotopy theory and in chromatic stable homotopy theory) are considered from this point of view. Status: Submitted for publication. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees/guanajuato Title: Local cohomology in equivariant topology Author: J.P.C.Greenlees AMS classification numbers: 13D45, 19L41, 20Jxx, 55N91, 55N22, 55P43 Address: University of Sheffield, UK Email: j.greenlees@shef.ac.uk Abstract: The article (based on talks at the Guanajuato Workshop on Local Cohomology, December 1999) describes the role of local homology and cohomology in understanding the equivariant cohomology and homology of universal spaces. This brings to light an interesting duality property related to the Gorenstein condition. The phenomena are studied and illustrated in several rather different families of examples. Both topology and commutative algebra benefit from the connection, and many interesting questions remain open. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees/so3q Title: Rational SO(3)-equivariant cohomology theories Author: J.P.C.Greenlees AMS classification numbers: 55N91, 55P42, 55P62, 55P91 Address: University of Sheffield, UK Email: j.greenlees@shef.ac.uk Abstract: The results of previous work for the circle and O(2) are used to give an explicit algebraic model of the category of rational SO(3)-spectra. This gives a complete classification of rational SO(3)-equivariant cohomology theories. A number of new features appear for the first time for this group. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees-Hopkins-Rosu/ellT Title: Rational S^1-equivariant elliptic cohomology Authors:J.P.C.Greenlees, M.J.Hopkins and I.Rosu AMS Class numbers: 55N34, 55N91, 55P42, 55P62 \address{JPCG: Department of Pure Mathematics, Hicks Building, Sheffield S3 7RH. UK.} \email{j.greenlees@sheffield.ac.uk} \address{MJH: Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA.} \email{mjh@math.mit.edu} \address{IR: Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA.} \email{ioanid@math.mit.edu} Abstract: We give a functorial construction of a rational $S^1$-equivariant cohomology theory from an elliptic curve equipped with suitable coordinate data. The elliptic curve may be recovered from the cohomology theory; indeed, the value of the cohomology theory on the compactification of an $S^1$-representation is given by the sheaf cohomology of a suitable line bundle on the curve. The construction is easy: by considering functions on the elliptic curve with specified poles one may write down the representing $S^1$-spectrum in the first author's algebraic model of rational $S^1$-spectra. ---------------------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.