BABYL OPTIONS: -*- rmail -*- Version: 5 Labels: Note: This is the header of an rmail file. Note: If you are seeing it in rmail, Note: it means the file has no messages in it.  1, filed, edited, forwarded,, Mail-from: From hovey@math.mit.edu Fri Feb 3 09:53:22 1995 Return-Path: Received: from nevanlinna.mit.edu by math.mit.edu (4.1/Math-2.0) id AA23567; Fri, 3 Feb 95 09:51:15 EST From: Mark Hovey Received: by nevanlinna.mit.edu; Fri, 3 Feb 95 09:51:11 EST Date: Fri, 3 Feb 95 09:51:11 EST Message-Id: <9502031451.AA21474@nevanlinna.mit.edu> To: hovey@math.mit.edu Subject: Hopf mailing list Reply-To: hovey@math.mit.edu *** EOOH *** Return-Path: From: Mark Hovey Date: Sun, 18 Aug 96 09:51:11 EST To: hovey@math.mit.edu Subject: Hopf mailing list Reply-To: hovey@math.mit.edu We have five new papers again this time. Mark Hovey Papers uploaded to Hopf between Nov 1,1996 and Nov 18, 1996: 1. /pub/Buchstaber-Ray/decfmqd ABSTRACT FOR: DOUBLE COBORDISM, FLAG MANIFOLDS, AND QUANTUM DOUBLES Victor M Buchsaber and Nigel Ray Drinfeld's construction of quantum doubles is one of several recent advances in the theory of Hopf algebras (and their actions on rings) which may be attractively presented within the framework of complex cobordism; these developments were pioneered by S P Novikov and the first author. Here we extend their programme by discussing the geometric and homotopy theoretical interpretations of the quantum double of the Landweber-Novikov algebra, as represented by a subalgebra of operations in double complex cobordism. We base our study on certain families of bounded flag manifolds with double complex structure, originally introduced into cobordism theory by the second author. We give background information on double complex cobordism, and discuss the cell structure of the flag manifolds by analogy with the classic Schubert decomposition, allowing us to describe their complex oriented cohomological properties (already implicit in the Schubert calculus of Bressler and Evens). This yields a geometrical realization of the basic algebraic structures of the dual of the Landweber-Novikov algebra, as well as its quantum double. We work in the context of Boardman's eightfold way, which clarifies the relationship between the quantum double and the standard machinery of Hopf algebroids of homology cooperations. 2. /pub/Dwyer/Exotic.Cohomology.GLnZhalf Exotic cohomology for GL(n,Z[1/2]) by W. G. Dwyer We show that for n=32 the mod 2 group cohomology of GL(n,Z[1/2]) is not detected on the subgroup of diagonal matrices. This disproves an old conjecture, and suggests that the cohomology of these general linear groups may in general be difficult to understand. 3. /pub/Green-Leary/SpectrumChern Title: The spectrum of the Chern subring Authors: David J. Green, IEM Essen, Germany. david@exp-math.uni-essen.de Ian J. Leary, Univ. of Southampton, UK. ijl@maths.soton.ac.uk Status: Submitted for publication. Abstract: For certain subrings of the mod-$p$-cohomology of a compact Lie group, we give a description of the spectrum, analogous to Quillen's description of the spectrum of the whole cohomology ring. Subrings to which our theorem applies include the Chern subring. Corollaries include a characterization of those groups for which the Chern subring is F-isomorphic to the cohomology ring. 1991 Classification: Primary 20J06; Secondary 20D15, 55R40. 4. /pub/Green-Minh/gm_transfer Title: Transfer and Chern Classes for Extraspecial $p$-Groups Authors: David J. Green, IEM Essen, Germany. david@exp-math.uni-essen.de Pham Anh Minh, University of Hue, Vietnam. Status: Submitted for publication Abstract: In the cohomology ring of an extraspecial $p$-group, the subring generated by Chern classes and transfers is studied. This subring is strictly larger than the Chern subring, but still not the whole cohomology ring, even modulo nilradical. A formula is obtained relating Chern classes to transfers. 1991 Classification: Primary 20J06; Secondary 20D15, 55R40. 5. /pub/Hung-Peterson/spherical Spherical classes and the Dickson algebra Nguyen H. V. Hu'ng and Franklin P. Peterson We attack the conjecture that the only spherical classes in the homology of $Q_0S^0$ are Hopf invariant one and Kervaire invariant one elements. We do this by computing products in the $E^2$-term of the unstable Adams spectral sequence converging to $\pi_*(Q_0S^0)$ using results about the Dickson algebra and by studying the Lannes--Zarati homomorphism. ---------------------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.mit.edu/~hovey/ If this doesn't work or is missing a few issues, try http://www.lehigh.edu/~dmd1/public/www-data/algtop.html , which also has the other messages sent to Don's list. To get the papers listed above, point your WWW client (Mosaic, Netscape) to http://hopf.math.purdue.edu/pub/hopf.html There are links to conference announcements, Purdue seminars, and other math related things on this page as well. You can also use 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. To do this take the TeX file and save the abstract to a different file, without any \begin{document} commands or anything, and transfer that file. You can use ascii instead of binary for this. I am solely responsible for this mailing list---don't send complaints about it to Clarence. Thanks to Clarence for creating and maintaining the archive.