Subject: new Hopf listings From: Mark Hovey Date: 01 Mar 2006 08:58:23 -0500 There are 4 new papers this time, from BrownR, DavisDaniel, DavisD, and Hovey. Mark Hovey New papers appearing on hopf between 2/8/06 and 3/1/06 1. http://hopf.math.purdue.edu/cgi-bin/generate?/BrownR/bedlewo Title: Three themes in the work of Charles Ehresmann: Local-to-global; Groupoids; Higher dimensions. Author: Ronald Brown AMS classification number: 01A60,53C29,81Q70,22A22,55P15 Expansion of an invited talk given to the 7th Conference on the Geometry and Topology of Manifolds: The Mathematical Legacy of Charles Ehresmann, Bedlewo 8.05.2005-15.05.2005 (Poland). Abstract: This paper illustrates the themes of the title in terms of: van Kampen type theorems for the fundamental groupoid; holonomy and monodromy groupoids; and higher homotopy groupoids. Interaction with work of the writer is explored. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/DavisDaniel/cplx2 Title: The E_2-term of the descent spectral sequence for continuous G-spectra Author: Daniel G. Davis Author's address: Purdue University Abstract: Let {X_i} be a tower of discrete G-spectra, each of which is fibrant as a spectrum, so that X=holim_i X_i is a continuous G-spectrum, with homotopy fixed point spectrum X^{hG}. The E_2-term of the descent spectral sequence for \pi_*(X^{hG}) cannot always be expressed as continuous cohomology. However, we show that the E_2-term is always built out of a certain complex of spectra, that, in the context of abelian groups, is used to compute the continuous cochain cohomology of G with coefficients in lim_i M_i, where {M_i} is a tower of discrete G-modules. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/DavisD/CPcrabb4 Some new immersion results for complex projective space Donald M. Davis Lehigh University, Bethlehem, PA 18015 Abstract: We prove the following two new optimal immersion results for complex projective space. First, if n equiv 3 mod 8 but n not equiv 3 mod 64, and alpha(n)=7, then CP^n can be immersed in R^{4n-14}. Second, if n is even and alpha(n)=3, then CP^n can be immersed in R^{4n-4}. Here alpha(n) denotes the number of 1's in the binary expansion of n. The first contradicts a result of Crabb, who said that such an immersion does not exist, apparently due to an arithmetic mistake. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Hovey/injective-comod Injective comodules and Landweber exact homology theories Mark Hovey Wesleyan University Middletown, CT We classify the indecomposable injective E(n)_{*}E(n)-comodules, where $E(n)$ is the Johnson-Wilson homology theory. They are suspensions of the J_{n,r}, where J_{n,r} is the E(n)-homology of the rth monochromatic piece M_{r} E(r) of E(r) and $0\leq r\leq n$. The endomorphism ring of J_{n,r} is the ring of operations in the completed E(r) theory; this ring of operations is not really known so far as I know, though it is closely related to the stabilizer group S_r. An interesting byproduct of this study is the isomorphism E^{*}(X) = \Hom_{E(n)_{*}} (E(n)_{*}M_{n}X, K) where E is completed E(n) theory and K is the n-fold desuspension of E(n)_{*}/I_{n}^{\infty}). ---------------------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.