Subject: new Hopf listings Date: 18 Jun 2003 11:29:19 -0400 From: Mark Hovey I had to do some hand editing of abstracts this time, so remember to include author's name and title of paper with the abstract, at the least. It is also suggested that you include author's e-mail and AMS subject classifications. 7 new papers this time, from Andersen-Bauer-Grodal-Pedersen, Baas-Dundas-Rognes, Granja, Grojnowski (this is his old paper about equivariant elliptic cohomology), Hornbostel, Kuhn, and Morava. Mark Hovey New papers appearing on hopf between 5/17/03 and 6/18/03 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Andersen-Bauer-Grodal-Pedersen/loopnotlie Title: A finite loop space not rationally equivalent to a compact Lie group Authors: Kasper K. S. Andersen, Tilman Bauer, Jesper Grodal, Erik K. Pedersen Subj-class: Algebraic Topology; Geometric Topology MSC-class: 55P35; 55P15, 55R35 Comments: 8 pages, arXiv : math.AT/0306234 We construct a connected finite loop space of rank $66$ and dimension $1254$ whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than $66$ is in fact rationally equivalent to a compact Lie group, extending the classical known bound of $5$. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Baas-Dundas-Rognes/segal60 Title of Paper: Two-vector bundles and forms of elliptic cohomology Authors: Nils A. Baas, Bjorn I. Dundas and John Rognes Addresses of Authors: Department of Mathematical Sciences The Norwegian University of Science and Technology NO-7491 Trondheim Norway Department of Mathematical Sciences The Norwegian University of Science and Technology NO-7491 Trondheim Norway Department of Mathematics University of Oslo NO-0316 Oslo Norway Email address of Authors: baas@math.ntnu.no, dundas@math.ntnu.no and rognes@math.uio.no In this paper we define 2-vector bundles as suitable bundles of 2-vector spaces over a base space, and compare the resulting 2-K-theory with the algebraic K-theory spectrum K(V) of the 2-category of 2-vector spaces, as well as the algebraic K-theory spectrum K(ku) of the connective topological K-theory spectrum ku. We explain how K(ku) detects v_2-periodic phenomena in stable homotopy theory, and as such is a form of elliptic cohomology. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Granja/notehpn Title: Self maps of HP^n via the unstable Adams spectral sequence Authors: Gustavo Granja AMS Classification numbers: 55S35,55S36,55S37 Address of Author: Departamento de Matematica Instituto Superior Tecnico Av. Rovisco Pais 1049-001 Lisboa Portugal Email address of Author: ggranja@math.ist.utl.pt Abstract: We use obstruction theory based on the unstable Adams spectral sequence to construct self maps of finite quaternionic projective spaces. As a result, a conjecture of Feder and Gitler regarding the classification of self maps up to homology is proved in two new cases. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Grojnowski/deloc Delocalized equivariant elliptic cohomology by Ian Grojnowski This is an old paper, which has been circulating quietly for almost a decade. It contains a definition of an equivariant elliptic cohomology theory for compact connected Lie groups and reasonable topological spaces. The theory is defined over Q, i.e. neglects torsion completely, and yet was still interesting. This is because of the well known heuristic identifying elliptic cohomology with something like the K-theory of the loop space. The functor of "loops into" is not local---there is no Mayer-Vietoris style patching. Yet elliptic cohomology has such a property. However the equivariant elliptic cohomology defined here does not satisfy such a naive locality propery. Instead, the elliptic cohomology of a space is a non-trivial bundle on the canonical abelian variety associated to the group. The crudest invariant of such a bundle is its first Chern class. This is a combinatorial shadow of the failure of locality. These same obstruction invariants occur in the study of semi-infinite D-modules on the infinitesimal neighbourhood of formal loops in the loop space of an algebraic variety; just as one would expect. -- Since this paper was written there have been several developments. Rosu and Ando used this theory to give a new proof of Witten rigidity, and Greenlees constructed a model for that part of rational equivariant S^1 homotopy that is seen by an elliptic cohomology theory. (There has also been the extraordinary work of Hopkins et al on tmf). 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Hornbostel/Motchrom Chromatic motivic homotopy theory by Jens Hornbostel We construct a motivic version of the chromatic filtration and the chromatic spectral sequence. This should be used to study the stable ${\bf A}^1$-homotopy groups of the motivic sphere spectrum. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Kuhn/Kuhn Title: Localization of Andre--Quillen--Goodwillie towers, and the periodic homology of infinite loopspaces Author: Nicholas J. Kuhn AMS classification numbers: 55P43, 55P47, 55N20, 18G55 Address: Department of Mathematics, University of Virginia, Charlottesville, VA 22903 email: njk4x@virginia.edu abstract: Let K(n) be the nth Morava K--theory at a prime p. This paper is a thorough study of questions like the following: to what extent does the K(n)--localization, or the K(n)--homology, of a spectrum X determine the K(n)--homology of its 0th space X_0? Our methods combine techniques from modern homotopical algebra with chromatic homotopy. In particular, we use the telescopic functors of Bousfield and the author (dependent on the Nilpotence Theorem of Devanitz, Hopkins, and Smith), as well as Topological Andre--Quillen Homology and Goodwillie calculus in nonconnective settings. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Morava/SegalMS Heisenberg groups and algebraic topology by Jack Morava This paper overlaps considerably with earlier, sketchier papers about the Tate cohomology of circle actions and its connection to Heisenberg groups. It will appear in the Segal Festschrift: We study the Madsen-Tillmann spectrum $\C P^\infty_{-1}$ as a quotient of the Mahowald pro-object $\C P^{\infty}_{-\infty}$, which is closely related to the Tate cohomology of circle actions. That theory has an associated symplectic structure, whose symmetries define the Virasoro operations on the cohomology of moduli space constructed by Kontsevich and Witten. ---------------------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.