Subject: new Hopf listings From: Mark Hovey Date: 26 Apr 1999 02:55:22 -0400 I am happy to announce that Wesleyan has offered me a tenure-track job, with the tenure decision in the third year. Algebraic topology's longest running soap opera ends at last! In case you hadn't heard, the second-longest running soap opera is also over; John Palmieri is going to the University of Washington, with the same deal as mine at Wesleyan. Matthew and Amy Ando are going to the University of Illinois. A wonderful spring! 7 new papers this time. Note that papers by Larry Smith are currently separated into two directories--LSmith and SmithL. According to Clarence, these will be merged into SmithL. Mark Hovey New papers uploaded to hopf between 4/8/99 and 4/23/99. 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Dehon-Lannes/DL Title : Sur les espaces fonctionnels dont la source est le classifiant d'un groupe de Lie compact commutatif Authors : Fran\c{c}ois-Xavier Dehon et Jean Lannes Address : Centre de Math\'ematiques, UMR 7640 du CNRS, Ecole Polytechnique, 91128 Palaiseau cedex, France E-mail : dehon@math.polytechnique.fr lannes@math.polytechnique.fr Abstract : We show in this paper how the acquired knowledge on the mapping spaces with source the classifying space of $\mathbb{Z}/p$ (\cite{La2}, \cite{DS}) and the use of unstable $\mathrm{MU}$-resolutions give results on the mapping spaces with source the classifying space of a finite abelian $p$-group or a torus if the target space is required to have a torsion free p-adic cohomology. We prove among other things that the set of homotopy classes of maps from the classifying space $X$ of a torus to some simply connected space $Y$ whose ordinary homology is null in odd degrees and a finite dimensional free abelian group in each even degree, and whose rational cohomology is polynomial, identifies with the set of maps from the K-theory of $Y$ to the K-theory of $X$ which preserve the $\lambda$-ring structure. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Green-Leary-Schuster/gls Title: The subring of group cohomology constructed by permutation representations Authors: David J. Green (green@math.uni-wuppertal.de) Ian J. Leary (ijl@maths.soton.ac.uk) Bj"orn Schuster (schuster@math.uni-wuppertal.de) Date: 21 April 1999 Status: Submitted for publication Abstract: Each permutation representation of a finite group $G$ can be used to pull cohomology classes back from a symmetric group to $G$. We study the ring generated by all classes that arise in this fashion, describing its variety in terms of the subgroup structure of $G$. We also investigate the effect of restricting to special types of permutation representations, such as $GL_n(F_p)$ acting on flags of subspaces. 1991 Mathematics Subject Classification: 20J06 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Lueck-Meintrup/lm Title: The Type of the Classifying Space of a Topological Group for the Family of Compact Subgroups Authors: Wolfgang Lueck and David Meintrup classification number: 55R35 Addresses: Wolfgang Lueck and David Meintrup Institut fuer Mathematik und Informatik Westfaelische Wilhelms-Universtitaet Einsteinstr. 62, 48149 Muenster, Germany e-mail: lueck@math.uni-muenster.de, meintrd@math.uni-muenster.de http://wwwmath.uni-muenster.de/math/u/lueck EPS or PS files: none Text of Abstract: Let G be a locally compact topological group. We investigate the type of the classifying space of G for the family of compact subgroups. We give criteria for this space to have a d-dimensional G-CW-model, a finite G-CW-model or a G-CW-model of finite type. Essentially we reduce these questions to discrete groups and to the homological algebra of the orbit category of discrete groups with respect to certain families of subgroups. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Schwede/stable `Stable homotopy of algebraic theories' to appear in Topology Stefan Schwede Fakultaet fuer Mathematik Universitaet Bielefeld 33615 Bielefeld, Germany schwede@mathematik.uni-bielefeld.de ABSTRACT: The simplicial objects in an algebraic category admit an abstract homotopy theory via a Quillen model category structure. We show that the associated stable homotopy theory is completely determined by a ring spectrum functorially associated with the algebraic theory. For several examples of algebraic theories the parameterizing ring spectrum can be identified with something familiar: for the theory of sets we obtain the standard model of the sphere spectrum; the theories of monoids and groups give different, but stably equivalent models for the sphere spectrum; for sets with an action of a fixed groups one gets the spherical group ring; the theory of modules over a fixed ring leads to the Eilenberg-MacLane ring spectrum. For many other algebraic theories we obtain new examples of ring spectra. For the theory of commutative algebras we obtain a ring spectrum which is related to Andre-Quillen homology via certain spectral sequences. We show that the (co-)homology of an algebraic theory is isomorphic to the topological Hochschild (co-)homology of the parameterizing ring spectrum. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/SmithL/t-fun Title: Lannes T-Functor and Invariants of Pointwise Stabilizers Author: Larry Smith AMSCodes: 13A50 Invariant Theory, 55S10 Steenrod Algebra Email: larry@sunrise.uni-math.gwdg.de This is a PostScript file!! Abstract: Let rho : G ---> GL(n, F) be a representation of a finite group G over the field F. The group G acts on the algebra of polynomial functions F[V] on V via rho and the subalgebra of polynomials invariant under this action is denoted by F[V]^G. If U subseteq V = F^n is a linear subspace then the pointwise stabilizer of U is denoted by G_U. In this note we examine the relation between F[V]^G (the subalgebra of invariant polynomials) and F[V]^{G_U} when F is a Galois field. We do so using the T-functor introduced by J. Lannes. What we show is that a wide variety of properties of F[V]^G are inherited by F[V]^{G_U}. For example, among other things: --- we reprove a result of H. Nakajima that F[V]^{G_U} is a polynomial algebra when F[V]^G is; --- we show that the Cohen-Macaulay property is inherited by F[V]^{G_U} from F[V]^G; --- and, when F[V]^G is a complete intersection, then so is F[V]^{G_U}. We apply the T-functor to study degree bounds for generators of rings of invariants, show how the T-functor relates to the transfer homomorphism Tr^G : F[V] ---> F[V]^G, and give an application in the modular case. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/SmithL/talgebra Title: On Lannes T-Functor Author: Larry Smith AMSCodes: 55S10 Steenrod Algebra Email: larry@sunrise.uni-math.gwdg.de This is a PostScript file!! Abstract: Let K denote the category of unstable algebras over the Steenrod algebra A^*. In connection with the study of the cohomology of function spaces J. Lannes introduced a remarkable functor T_U : K wigglyrightarrow K depending on a finite dimensional vector space U over the prime field. The purpose of this note is to prove some basic facts concerning how T_U relates to many of the standard properties of commutative algebras, such as Noetherean, polynomial, Cohen-Macaulay, etc. Some of the results proved here are already known, and some not. In all cases the proofs are new. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/SmithL/variety Title: Variations on a Theroem of Haynes R. MIller and a Functor of Jean Lannes Author: Larry Smith AMS Codes: 55S10 Steenrod Algebra, 13A50 Invaraint Theory Email: larry@sunrise.uni-math.gwdg.de This is a PostScript file!! Abstract: Recent advances in modular invariant theory have often made use of Steenrod operations and the T-functor introduced by Jean Lannes. Many key properties of this functor depend on a Theorem of Haynes Miller. These results have been proved by a mixture of algebraic and topological methods for the full algebra of cohomology operations, and hence are only proven for the prime field F_p. Until now, for odd primes, it is not the algebra of cohomology operations that enters invariant theory, but the subalgebra of reduced powers. Deriving from the known results, those needed for invariant theory is sometimes not so obvious. This is a technical manuscript, providing proofs, over an arbitrary Galois field, of those key properties of unstable algebras over the Steenrod algebra that are essential to modular invariant theory. Being technical, it goes without saying that we assume a familiarity with some version of the Steenrod algebra, be it topological, as in the classical book of Steenrod and Epstein, or algebraic as in my book Polynomial Invariants of Finite Groups, AK Peters Ltd. 1996. ---------------------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 -------