Subject: new Hopf listings From: Mark Hovey Date: 14 May 2007 09:05:17 -0400 4 new papers this month, from Barge-Lannes, Biedermann, Bubenik, and Devinatz. Mark Hovey New papers appearing on hopf between 4/19/07 and 5/14/07 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Barge-Lannes/SMB Title: Suites de Sturm, indice de Maslov et p\'e riodicit\'e de Bott Authors: Jean Barge and Jean Lannes Abstract: This memoir presents a reworking of a very classical subject; it is related to works of many people, especially: Richard W. Sharpe, Max Karoubi, Andrew Ranicki, Fran\c{c}ois Latour... We explain in particular how the usual theory of Sturm sequences is linked to the fundamental theorem of hermitian K-theory (due to Karoubi) and to Bott periodicity. Keywords: Sturm sequences, Maslov index, Bott periodicity, hermitian K-theory. AMS classification: 19G38, 19C99. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Biedermann/L-stable L-stable functors by Georg Biedermann We generalize and greatly simplify the approach of Lydakis and Dundas-R\"ondigs-{\O}stv{\ae}r to construct an L-stable model structure for small functors from a closed symmetric monoidal model category V to a V-model category M, where L is a small cofibrant object of V. For the special case V=M=S_* pointed simplicial sets and L=S1 this is the classical case of linear functors and has been described as the first stage of the Goodwillie tower of a homotopy functor. We show, that our various model structures are compatible with a closed symmetric monoidal product on small functors. We compare them with other L-stabilizations described by Hovey, Jardine and others. This gives a particularly easy construction of the classical and the motivic stable homotopy category with the correct smash product. We establish the monoid axiom under certain conditions. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Bubenik/sep Author: Peter Bubenik Title: Separated Lie models and the homotopy Lie algebra AMS classification number: Primary 55P62; Secondary 17B55 to appear in the Journal of Pure and Applied Algebra Abstract: The homotopy Lie algebra of a simply connected topological space, X, is given by the rational homotopy groups on the loop space of X. Following Quillen, there is a connected differential graded free Lie algebra (dgL) called a Lie model, which determines the rational homotopy type of X, and whose homology is isomorphic to the homotopy Lie algebra. We show that such a Lie model can be replaced with one that has a special property we call separated. The homology of a separated dgL has a particular form which lends itself to calculations. We give connections to the radical of the homotopy Lie algebra and the Avramov-Felix conjecture. Examples that are worked out in detail include wedges of spheres on any "thickness" and connected sums of products of spheres. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Devinatz/towardsfiniteness Title: Towards the finiteness of the homotopy groups of the K(n)-localization of S0. Author: Ethan S. Devinatz Abstract: Let G be a closed subgroup of the nth Morava stabilizer group S_n, n>1, and let E_n^{hG} denote the continuous homotopy fixed point spectrum of Devinatz and Hopkins. If G=, the subgroup topologically generated by an element z in the p-Sylow subgroup S_n0 of S_n, and z is non-torsion in the quotient of S_n0 by its center, we prove that the E_n^{h}-homology of any K(n-2)-acyclic finite spectrum annihilated by p is of essentially finite rank. (The definition of essentially finite rank is given in the paper.) We also show that the units in the coefficient ring of E_n which are fixed by z are just the units in the Witt vectors with coefficients in the field of p^n elements. If n=2 and p>3, we show that, if G is a closed subgroup of S_n0 not contained in the center, then G contains an open subnormal subgroup U such that the mod(p) homotopy of E_n^{hV} is of essentially finite rank, where V is the product of U with the units in the field of p elements. ---------------------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 should submit 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 at math.purdue.edu telling him what you have uploaded. The largest archive of math preprints is at http://arxiv.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 the arXiv, send e-mail to math@arxiv.org with subject line "subscribe" (without quotes), and with the body of the message "add AT" (without quotes). I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive.