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, edited,, Mail-from: From dmd1@lehigh.edu Sat Jan 17 18:19:15 1998 Received: from nss4.cc.Lehigh.EDU (root@nss4.CC.Lehigh.EDU [128.180.1.13]) by mail.wesleyan.edu (8.8.6/8.7.3) with ESMTP id SAA10234 for ; Sat, 17 Jan 1998 18:20:52 -0500 (EST) Received: from ns4-1.CC.Lehigh.EDU (root@ns4-1.CC.Lehigh.EDU [128.180.1.42]) by nss4.cc.Lehigh.EDU (8.8.8/8.8.5) with ESMTP id SAA119110; Sat, 17 Jan 1998 18:23:02 -0500 Received: (from dmd1@localhost) by ns4-1.CC.Lehigh.EDU (8.8.5/8.8.5) id SAA39528; Sat, 17 Jan 1998 18:19:17 -0500 Message-Id: <199801172319.SAA39528@ns4-1.CC.Lehigh.EDU> Date: Sat, 17 Jan 1998 18:19:15 EST From: dmd1@lehigh.edu (DONALD M. DAVIS) X-Mailer: SENDM [Version 2.0.17] Subject: new Hopf listings To: Distribution.List@lehigh.edu (toplist) Content-Type: text X-UIDL: aacd4710beaa4a6483935a131ded8f1b Lines: 256 Xref: picard.math.wesleyan.edu davis:291 X-Gnus-Newsgroup: davis:291 Sun Jan 18 06:29:52 1998 *** EOOH *** Date: Sat, 17 Jan 1998 18:19:15 EST From: dmd1@lehigh.edu (DONALD M. DAVIS) X-Mailer: SENDM [Version 2.0.17] Subject: new Hopf listings To: Distribution.List@lehigh.edu (toplist) Content-Type: text X-UIDL: aacd4710beaa4a6483935a131ded8f1b Lines: 256 Xref: picard.math.wesleyan.edu davis:291 X-Gnus-Newsgroup: davis:291 Sun Jan 18 06:29:52 1998 11 new papers this time. Mark Hovey New papers uploaded to hopf between 4/24/99 and 5/17/99. 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Boardman-Kramer-Wilson/boardman-kramer-wilson Title: The Periodic Hopf Ring of Connective Morava K-Theory Authors: J. Michael Boardman Richard L. Kramer W. Stephen Wilson Address: Department of Mathematics Johns Hopkins University Baltimore, Maryland 21218 Email: jmb@math.jhu.edu wsw@math.jhu.edu} Abstract: Let $K(n)_*(-)$ denote the $n$-th periodic Morava K-theory for any fixed odd prime $p$. Let $\underline{k(n)}_{\:*}$ denote the $\Omega$-spectrum of the $n$-th connective Morava K-theory. We give a calculation of the Hopf ring $K(n)_*\underline{k(n)}_{\:*}$, the main result of the second author's thesis. This is a new, shorter, easier proof. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Boardman-Wilson/boardman-wilson-easy-split Title: Unstable splittings related to Brown-Peterson cohomology Authors: J. Michael Boardman W. Stephen Wilson Address: Johns Hopkins University Baltimore, Maryland 21218 Email: jmb@math.jhu.edu wsw@math.jhu.edu Abstract: A new and relatively easy proof of various unstable splittings associated with Brown-Peterson cohomology is presented. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Cohen-Jones-Segal/holmorse Stability for holomorphic spheres and Morse theory by Ralph L. Cohen, John D.S. Jones, and Graeme B. Segal AMS Classification numbers: 57R19, 58fF09, 32H02 Addresses of Authors: Cohen: Dept. of Mathematics, Stanford University, Stanford, Ca. 94305 Jones: Dept. of Mathematics, University of Warwick, Coventry, England Segal: Dept. of Pure Math. and Math. Statistics, Cambridge University, Cambridge, England Email addresses of Authors: Cohen: ralph@math.stanford.edu Jones: jdsj@maths.warwick.ac.uk Segal: G.B.Segal@dpmms.cam.ac.uk In this paper we study the question of when does a closed, simply connected, integral symplectic manifold $(X, \omega)$ have the "stability property" for its spaces of based holomorphic spheres? This property states that in a stable limit under certain gluing operations, the space of based holomorphic maps from a sphere to $X$, becomes homotopy equivalent to the space of all continuous maps, lim_k Hol_k(S^2, X) = \Omega^2 X Here "=" means homotopy equivalent. The "degree k" is the evaluation of the integral cohomology class represented by the symplectic form on the map S^2 --> X. We describe this limit as a kind of group completion of Hol(S^2, X). We conjecture that this stability property holds if and only if an evaluation map $E: lim_k Hol_k(S^2, X) ---> X is a quasifibration. In this paper we will prove that in the presence of this quasifibration condition, then the stability property holds if and only if the Morse theoretic flow category of the symplectic action functional on the universal cover of the loop space, LX, has a classifying space that realizes the homotopy type of LX. We conjecture that in the presence of this quasifibration condition, this Morse theoretic condition always holds. We will prove this in the case of X a homogeneous space, thereby giving an alternate proof of the stability theorem for holomorphic spheres for a projective homogeneous variety originally due to Gravesen. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Cole-Greenlees-Kriz/AThom The universality of equivariant complex bordism \author{Michael Cole} \address{Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-0001} \email{mmcole@math.lsa.umich.edu} \author{J.P.C.Greenlees} \address{School of Mathematics and Statistics, Hicks Building, Sheffield S3 7RH. UK.} \email{j.greenlees@sheffield.ac.uk} \author{I.Kriz} \address{Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1003} \email{ikriz@math.lsa.umich.edu} We show that if $A$ is an abelian compact Lie group, all $A$-equivariant complex vector bundles are orientable over a complex orientable equivariant cohomology theory. In the process, we calculate the complex orientable homology and cohomology of all complex Grassmannians, and thereby establish that complex orientability corresponds to the existence of a map from $MU$ to the spectrum as in the non-equivariant case. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees/LAm \title{Multiplicative equivariant formal group laws.} \author{J.P.C.Greenlees} \address{School of Mathematics and Statistics, Hicks Building, Sheffield S3 7RH. UK.} \email{j.greenlees@sheffield.ac.uk} The notion of an $A$-equivariant formal group law for a compact abelian Lie group $A$ was introduced to study complex oriented $A$-equivariant formal group laws, but has some intrinsic algebraic interest. The theorem that the coefficient ring of equivariant complex bordism is the universal ring for equivariant formal group laws establishes that the definition is the correct one. We shall be concerned here with a very special class of equivariant formal group laws: the multiplicative ones, which appear to play a privileged role amongst all equivariant formal group laws. However our principal motivation for considering this case is its importance in understanding equivariant K-theories, and its close relationship to representation theory. The universal ring for multiplicative equivariant formal group laws is shown to be closely related to the Rees ring of the representation ring at the augmentation ideal, but only equal to it if the group is topologically cyclic. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees-Lyubeznik/ringlct \title{Rings with a local cohomology theorem and applications to cohomology rings of groups.} \author{J.P.C.Greenlees} \address{Department of Pure Mathematics, Hicks Building, Sheffield, S3 7RH, UK.} \email{j.greenlees@sheffield.ac.uk} \author{G.Lyubeznik} \address{Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA} \email{gennady@math.umn.edu} It has recently emerged that the rings of coefficients of equivariant cohomology theories very often have remarkable duality properties. It is the purpose of the present paper to formulate the duality purely algebraically in a particularly favourable case (including the ordinary cohomology rings of discrete or profinite virtual duality groups and classifying spaces of compact Lie groups), and to investigate its ring theoretic implications. We formulate a purely algebraic form of this duality, and investigate its consequences. It is obvious that a Cohen-Macaulay ring of this sort is automatically Gorenstein, and that its Hilbert series therefore satisfies a functional equation, and our main result is a generalization of this to rings with depth one less than their dimension: this proves a conjecture of Benson and Greenlees. Structural counterparts of this are also proved, showing that these rings are very well behaved in codimension 0 and 1. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Iwase/coH-Ganea Title of Paper: Co-H-spaces and the Ganea conjecture Authors: Norio Iwase AMS Classification numbers: Primary 55P45 Addresses of Authors: Graduate School of Mathematics, Kyushu University, Ropponmatsu, Fukuoka 810-8560, Japan. Email addresses of Authors: iwase@math.rc.kyushu-u.ac.jp Text of Abstract: A non-simply connected co-H-space $X$ is, up to homotopy, the total space of a fibrewise-simply connected pointed fibrewise co-Hopf fibrant $j : X \to B\pi_1(X)$, which is a space with a co-action of $B\pi_1(X)$ along $j$. We construct its homology decomposition, which yields a simple construction of its fibrewise localisation. Our main goal is the construction of a series of co-H-spaces, each of which cannot be split into a one-point-sum of a bunch of circles and a simply connected space, thus disproving the Ganea conjecture. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Kashiwabara-Wilson/kashiwabara-wilson-cohomology Title: The Morava K-theory and Brown-Peterson cohomology of spaces related to BP Authors: Takuji Kashiwabara W. Stephen Wilson Addresses: Institut Fourier, Universit\'{e} de Grenoble I, U.M.R. au C.N.R.S., B. P. 74, 38402 Saint-Martin-d'H\`{e}res CEDEX France Department of Mathematics Johns Hopkins University Baltimore, Maryland 21218 and Department of Mathematics Kyoto University Kyoto 606-8502 Japan Emails: Takuji.Kashiwabara@ujf-grenoble.fr wsw@math.jhu.edu Abstract: We calculate the Morava K-theory of the spaces in the Omega spectra for BP. They fit into an exotic array of short and long exact sequences of Hopf algebras. We apply this to calculate the p-adically completed Brown-Peterson cohomology, as well as all of the intermediary cohomology theories, E, of these spaces. We give two descriptions of the answer, both of which turn out to be surprisingly nice. One part of our first description is just the image in the E cohomology of the corresponding space in the Omega spectrum for BP, which is as big as it could possibly be and which we show how to calculate. The other part is just the E cohomology of several copies of Eilenberg-MacLane spaces, something which is already known. Our second description is inductive and gives us a new way of looking at the Brown-Peterson cohomology of Eilenberg-MacLane spaces. The Brown-Comenetz dual of BP shows up in our calculations and so we take up the study of this spectrum as well. It was already known that the Morava K-theory of the spaces in the Omega spectrum for the Brown-Comenetz dual of BP made it look like a product of Eilenberg-MacLane spaces and we find, somewhat to our surprise, that the same is true for the BP cohomology. In order to state our answers we set up the foundations for the category of completed Hopf algebras. 9. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/LewisG/PrjFlt WHEN PROJECTIVE DOES NOT IMPLY FLAT, AND OTHER HOMOLOGICAL ANOMALIES L. GAUNCE LEWIS, JR. Department of Mathematics, Syracuse University, Syracuse NY 13244-1150 E-mail address: gaunce@ichthus.syr.edu Abstract. The category MG of Mackey functors for a group G carries a symmetric monoidal closed structure. The box product providing this structure encodes the Frobenius axiom, which describes the interaction of induction and multiplication in Mackey functor rings. Mackey functors are of interest in equivariant homotopy theory since good equivariant cohomology theories are Mackey functor valued. In this context, the box product is useful not only because it encodes the interaction between induction and the cup product, but also because of the role it plays in the not yet fully understood universal coefficient and K"unneth formulae. This role makes it important to know whether projective objects in MG are flat, and whether the box product of projective objects in MG is projective. In the most familiar symmetric monoidal abelian categories, the tensor product obviously interacts appropriately with projective objects. However, the box product for MG need not be so well behaved. For example, if G is O(n), projectives need not be flat in MG and the box product of projective objects need not be projective. This misbehavior complicates the search for full strength equivariant universal coefficient and K"unneth formulae. These questions about the interaction of the box product with projective objects can be regarded as compatibility conditions which may be satisfied by a symmetric monoidal closed category M. The primary purpose of this article is to investigate these, and related, conditions. Our focus is on functor categories whose monoidal structures arise in a fashion described by Day. Conditions are given under which such a structure interacts appropriately with projective objects. Further, examples are given to show that, when these conditions aren't met, this interaction can be quite bad. These examples were not fabricated to illustrate the abstract possibility of misbehavior. Rather, they are drawn from the literature. In particular, MG is badly behaved not only for the groups O(n), but also for the groups SO(n), U(n), SU(n), Sp(n), and Spin(n). Similar misbehavior occurs in two categories of global Mackey functors which are widely used in the study of classifying spaces of finite groups. 10. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Real/cupi I attach here the zip dvi.file of the paper ``A combinatorial method for computing Steenrod Squares'' which will be published this summer in JPAA. I would like that this paper would be included in Hopf archive. I think that this paper will completely answer the question raised by Prof. McClure in Algebraic Topology Discussion List about cup-i products. If you have problems with these files, please do not hesitate to contact me. Best regards, Pedro Pedro Real Dpto de Matematica Aplicada I Fac. de Informatica y estadistica Univ. de Sevilla Avda. Reina Mercedes s/n 41012 Sevilla Tfno: 34-95-4556921 Fax: 34-95-4557878 e-mail: real@cica.es 11. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/WilsonWS/wilson-hopf-rings-survey Title: Hopf rings in algebraic topology Author: W. Stephen Wilson Address: Johns Hopkins University Baltimore, Maryland 21218 Email: wsw@math.jhu.edu Abstract: These are colloquium style lecture notes about Hopf rings in algebraic topology. They were designed for use by non-topologists and graduate students but have been found helpful for those who want to start learning about Hopf rings. They are not ``up to date,'' nor are then intended to be, but instead they are intended to be introductory in nature. Although these are ``old'' notes, Hopf rings are thriving and these notes give a relatively painless introduction which should prepare the reader to approach the current literature. ---------------------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 (Mosaic, Netscape) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to conference announcements, 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/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.