Subject: new Hopf listings From: Mark Hovey Date: 22 Mar 1999 01:45:54 -0500 Here are the abstracts for those new papers Clarence annnounced. Nine new papers and a revision this time. Mark Hovey New papers uploaded to hopf between 2/14/99 and 3/22/99: 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Arone/Weiss The Weiss derivatives of $\BO(-)$ and $\BU(-)$ Gregory Arone University of Chicago arone@math.uchicago.edu We study Michael Weiss' ``orthogonal tower'' of the functors $V\mapsto \BO (V)$ and $V\mapsto \BU(V)$. We describe the Weiss derivatives of these functors and calculate the homology of the layers. The orthogonal tower studied here is related to the Goodwillie tower of the identity functor in various ways. We find that many of the results of Arone-Mahowald and Arone-Dwyer on the Goodwillie derivatives of the identity have interesting analogues in the context of the Weiss tower, but there are new things to be learned from it. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/BakerA/ss-isog (This one should be in Baker, with Andy's other papers, so will probably be moved there). Isogenies of supersingular elliptic curves over finite fields and operations in elliptic cohomology Andrew Baker Department of Mathematics, University of Glasgow a.baker@maths.gla.ac.uk http://maths.gla.ac.uk/~andy In this paper we investigate stable operations in supersingular elliptic cohomology using isogenies of supersingular elliptic curves over finite fields. Our main results provide a framework in which we give a conceptually simple new proof of an elliptic cohomology version of the Morava change of rings theorem and also gives models for explicit stable operations in terms of isogenies and morphisms in certain enlarged isogeny categories. We are particularly inspired by number theoretic work of G.~Robert, whose work we reformulate and generalize in our setting. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Broto-Moller/di2tof4 Title: Embeddings of DI2 in F4 Authors: Carles Broto and Jesper Moller AMS class: 55R12, 55P15 Address: Carles Broto Departament de Matematiques, Universitat Autonoma de Barcelona, 08193 Bellaterra, Spain e-mail: broto@manwe.mat.uab.es Address: Jesper Moller Matematisk Institut Universitetsparken 5 DK-2100 Copenhagen Denmark e-mail: moller@math.ku.dk Abstract: We show that at the prime 3, the Dickson space BDI2 is the homotopy fixed point space for an action of Z/2 on the BF4. We classify all embeddings of DI2 into F4. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Crossley-Whitehouse/conjinvs Title: On Conjugation Invariants in the dual Steenrod algebra Authors: M. D. Crossley and Sarah Whitehouse AMS Classification Numbers: 55S10, 20J06, 20C30 Addresses: Max-Planck-Institut fur Mathematik, P.O. Box 7280, D-53072 Bonn, Germany. Departement de Mathematiques, Universite d'Artois - Pole de Lens, Rue Jean Souvraz, S. P. 18 - 63207 Lens, France. Email addresses: crossley\@member.ams.org whitehouse\@poincare.univ-artois.fr Abstract Text: We investigate the canonical conjugation chi of the mod 2 dual Steenrod algebra with a view to determining the subspace of elements invariant under chi. We give bounds on the dimension of this subspace for each degree and show that, after inverting xi_1, it becomes polynomial on a natural set of generators. Finally we note that, without inverting this class, the invariant subspace is far from being polynomial. Note: This is a revised version of the paper of the same name we submitted last April. The only significant change is in section 5 where we withdraw a somewhat over-optimistic conjecture and correct some of the proofs. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Maltsiniotis/grpdq Groupoides quantiques de base non commutative Georges MALTSINIOTIS AMS : 16W30; 17B37; 22A22; 55U10 Universite Paris VII maltsin@math.jussieu.fr The aim of this paper is to introduce a notion of quantum groupoid, non-commutative analogue of Lie groupoids. This notion generalizes simultaneously the notion of a Hopf bigebroid (corresponding to a quantum groupoid with commutative space of units) and the notion of a braided quantum group of Majid. The commutativity hypothesis of the base is no more necessary and a construction of L. Vainerman enters in this frame. In order to achieve this, simplicial methods are used. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Neeman/triangulatedcats Title: Triangulated Categories Author: Amnon Neeman Address: School of Mathematical Sciences, The Australian National University, Canberra, ACT 0200, Australia. Email: amnon.neeman@anu.edu.au Abstract: The book begins from scratch. The first two chapters amount to an exposition of standard results. But the rest of the book develops the new notion of "well generated triangulated categories". We define them, and prove representability theorems for them. As an application, we deduce that, for any spectrum E, Brown's representability theorem holds in both the category of E-acyclic spectra, and the category of E-local spectra. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Oliver/2dim (This one is presumably also in the wrong place, headed for Oliver-Segev). Fixed point free actions on $Z$-acyclic 2-complexes by Bob Oliver and Yoav Segev AMS classification: primary 57S17, secondary 57M20, 20D05 Addresses: Laboratoire de Mathematiques Universite Paris-Nord Av. J-B Clement 93430 Villetaneuse, France Department of Mathematics Ben Gurion University Beer Sheva 84105, Israel E-mail: bob@math.univ-paris13.fr, yoavs@math.bgu.ac.il We show that a finite group has an "essential" fixed point free action on an acyclic 2-complex if and only if it is one of the simple groups in the following list: - $PSL_2(2^k)$ for $k\ge2$, - $PSL_2(q)$ for $q\equiv3,5$ (mod 8) and $q\ge5$, - $Sz(2^k)$ for odd $k\ge3$. More precisely, for any finite group $G$, and any 2-dimensional acyclic $G$-CW complex $X$ without fixed points, there is a normal subgroup $H$ in $G$ such that $G/H$ is in the above list, and such that the $G$-action on $X$ looks "essentially" like the $G/H$-action which we construct. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Oliver/lo2 (And this one must be headed for Luck-Oliver). Chern characters for equivariant $K$-theory of proper $G$-CW-complexes by Wolfgang L\"uck and Bob Oliver AMS classification: primary 55N91, secondary 19L47 Addresses: Institut f"ur Mathematik und Informatik Westf"alische Wilhelms-Universit"at Einsteinstr. 62 48149 M"unster, Germany Laboratoire de Mathematiques Universite Paris-Nord Av. J-B Clement 93430 Villetaneuse, France E-mail: lueck@math.uni-muenster.de, bob@math.univ-paris13.fr We first construct a classifying space for defining equivariant $K$-theory for proper actions of discrete groups. This is then applied to construct equivariant Chern characters with values in Bredon cohomology with coefficients in the representation ring functor $R(-)$ (tensored by the rationals). And this in turn is applied to prove some versions of the Atiyah-Segal completion theorem for real and complex $K$-theory of proper actions of discrete groups. 9. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Rudyak/NormalInvar On Sullivan's theorem of the normal invariant of homeomorphism. Yuli B. Rudyak In his paper about Hauptvermutung for manifolds (1967) Sullivan indicated the proof of the following theorem: Let h: M-->N be a homeomorphism of closed piecewise linear manifolds. Then the normal invariant of h is trivial provided 3-dimensional homology of M has no 2-torsion. The goal of this paper is to give a relative simple proof of this theorem in a particular case of manifolds M such that the fundamental and homology group of M are free abelian groups. Motivation: Kirby--Siebenmann proved that TOP/PL is the Eilenberg--Mac Lane space K(Z/2,3) and it actually solves the Hauptvermutung for manifolds. The proof by Kirby--Siebenmann uses a special case of the Normal Invariant Homeomorphism Theorem when M is the product of a torus with a sphere. 10. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Rudyak/ThomAdjoint On an adjoint functor to the Thom functor Yuli B. Rudyak We construct a right adjoint functor to the Thom functor, i.e., to the functor which assigns the Thom space T\xi to a vector bundle \xi. ---------------------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. ------- End of forwarded message -------