Subject: new Hopf listings From: Mark Hovey Date: 03 May 2006 11:05:07 -0400 There are 7 new papers this time, from Kuhn, Neusel-Sezer (2), Pengelley-Williams, RadulescuBanu, and SanchezGarcia (2) Mark Hovey New papers appearing on hopf between 4/7/06 and 5/3/06 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Kuhn/autgrp Title: The nilpotent filtration and the action of automorphisms on the cohomology of finite $p$--groups Author: Nicholas J. Kuhn AMS classification number: 20J06 Abstract: We study H^*(P), the mod p cohomology of a finite p--group P, viewed as an Out(P)--module. In particular, we study the conjecture, first considered by Martino and Priddy, that, if e_S in Z/p[Out(P)] is a primitive idempotent associated to an irreducible Z/p[Out(P)]--module S, then the Krull dimension of e_SH^*(P) equals the rank of P. The rank is an upper bound by Quillen's work, and the conjecture can be viewed as the statement that every irreducible Z/p[Out(P)]--module occurs as a composition factor in H^*(P) with similar frequency. In summary, our results are as follows. A strong form of the conjecture is true when p is odd. The situation is much more complex when p=2, but is reduced to a question about 2--central groups (groups in which all elements of order 2 are central), making it easy to verify the conjecture for many finite 2--groups, including all groups of order 128, and all groups that can be written as the product of groups of order 64 or less. Featured is the nilpotent filtration of the category of unstable A--modules. Also featured are unstable algebras of cohomology primitives associated to central group extensions. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Neusel-Sezer/noether-map-I The Noether Map I Mara D Neusel and M"ufit Sezer Abstract: Let $\rho: G\hookrightarrow GL(n, F)$ be a faithful representation of a finite group G. In this paper we study the image of the associated Noether map $ \eta_G^G: F[V(G)]^G \longrightarrow F[V]^G. $ It turns out that the image of the Noether map characterizes the ring of invariants in the sense that its integral closure $\overline{Im(\eta_G^G)} =F[V]^G$. This is true without any restrictions on the group, representation, or ground field. Moreover, we show that the extension $Im (\eta_G^G) \subseteq F[V]^G$ is a finite $p$-root extension. Furthermore, we show that the Noether map is surjective, i.e., its image integrally closed, if $V=F^n$ is a projective $FG$-module. We apply these results and obtain upper bounds on the degrees of a minimal generating set of $F[V]^G$ and the Cohen-Macaulay defect of $F[V]^G$. We illustrate our results with several examples. Note that this paper together with noether-map-II contain stronger results than the authors' previous paper Neusel-Sezer/noether. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Neusel-Sezer/noether-map-II The Noether Map II Mara D Neusel and M"ufit Sezer Abstract: Let $\rho: G\hookrightarrow GL(n, F)$ be a faithful representation of a finite group G. In this paper we proceed with the study of the image of the associated Noether map \[ \eta_G^G: F[V(G)]^G \longrightarrow F[V]^G. \] In [Noether Map I] it has been shown that the Noether map is surjective if $V$ is a projective $FG$-module. This paper deals with the converse. The converse is in general not true: we illustrate this with an example. However, for $p$-groups (where $p$ is the characteristic of the ground field $F$) as well as for permutation representations of any group the surjectivity of the Noether map implies the projectivity of $V$. Note that this paper together with noether-map-I contain stronger results than the authors' previous paper Neusel-Sezer/noether. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Pengelley-Williams/peng-will-oddkam The odd-primary Kudo-Araki-May algebra of algebraic Steenrod operations, and invariant theory David J. Pengelley and Frank Williams New Mexico State University Las Cruces, NM 88003 Primary 16W22; Secondary 16W30, 16W50, 55S10, 55S12, 55S99, 57T05. We describe bialgebras of lower-indexed algebraic Steenrod operations over the field with p elements, p an odd prime. These go beyond the operations that can act nontrivially in topology, and their duals are closely related to algebras of polynomial invariants under subgroups of the general linear groups that contain the unipotent upper triangular groups. There are significant differences between these algebras and the analogous one for p=2 , in particular in the nature and consequences of the defining Adem relations. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/RadulescuBanu/cofib-cat Title: Cofibrations in Homotopy Theory Author: Andrei Radulescu-Banu Author's mailing address: 86 Cedar St, Lexington, MA 02421 Abstract: We define Anderson-Brown-Cisisnski (ABC) cofibration categories, and construct homotopy colimits of diagrams of objects in ABC cofibraction categories. Homotopy colimits for Quillen model categories are obtained as a particular case. We attach to each ABC cofibration category a right derivator. A dual theory is developed for homotopy limits in ABC fibration categories and for left derivators. These constructions provide a natural framework for 'doing homotopy theory' in ABC (co)fibration categories. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/SanchezGarcia/bredon Title: Bredon homology and equivariant K-homology of SL(3,Z) Author: Ruben Sanchez-Garcia Author's address: Department of Pure Maths, Hicks Building University of Sheffield Sheffield S3 7RH, United Kingdom Included ps or eps files: SouleFundamentalDomainLabelled.eps TruncatedCube.eps AMS classification number: 19L47, 55N91 (Primary); 19K99, 46L80 (Secondary) Other useful information: arXiv:math.KT/0601587 Abstract: We obtain the equivariant K-homology of the classifying space \underline{E}SL(3,Z) from the computation of its Bredon homology with respect to finite subgroups and coefficients in the representation ring. We also obtain the corresponding results for GL(3,Z). Our calculations give therefore the topological side of the Baum-Connes conjecture for these groups. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/SanchezGarcia/coxeter Title: Equivariant K-homology for some Coxeter groups Author: Ruben Sanchez-Garcia Author's address: Department of Pure Maths, Hicks Building University of Sheffield Sheffield S3 7RH, United Kingdom Included eps files: hexagon3.eps hexagon4.eps interval.eps tessellation0.eps trianglesd2.eps AMS classification number: 19L47, 55N91 (Primary); 19K99, 46L80 (Secondary) Other useful information: arXiv:math.KT/0604402 Abstract: We obtain the equivariant K-homology of the classifying space \underline{E}W for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of \underline{E}W in terms of Coxeter cells. Our calculations amount to the K-theory of the reduced C^*-algebra of W, via the Baum-Connes assembly map. ---------------------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.