Subject: new Hopf listings From: Mark Hovey Date: 11 Nov 2005 08:43:11 -0500 There are 7 new papers this time, from Bartels-Reich, Bousfield, Fausk-Isaksen (2), Neusel, Neusel-Sezer, and Siebenmann. Mark Hovey New papers appearing on hopf between 10/1/05 and 11/11/05 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Bartels-Reich/erb Title: Coefficients for the Farrell-Jones Conjecture Authors: Arthur Bartels, Holger Reich Author's e-mail address: bartelsa@math.uni-muenster.de, reichh@math.uni-muenster.de Abstract: We introduce the Farrell-Jones Conjecture with coefficients in an additive category with G-action. This is a variant of the Farrell-Jones Conjecture about the algebraic K- or L-Theory of a group ring RG. It allows to treat twisted group rings and crossed product rings. The conjecture with coefficients is stronger than the original conjecture but it has better inheritance properties. Since known proofs using controlled algebra carry over to the set-up with coefficients we obtain new results about the original Farrell-Jones Conjecture. The conjecture with coefficients implies the fibered version of the Farrell-Jones Conjecture. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Bousfield/kunneth Title: Kunneth theorems and unstable operations in 2-adic KO-cohomology Author: A.K. Bousfield E-mail: bous@uic.edu AMS classifications: 55N15,55S25,55U25 Abstract: We develop Kunneth theorems and obtain detailed results on unstable operations in 2-adic KO-cohomology and, more generally, in united 2-adic K-cohomology. These results are needed for work on the K-localizations of H-spaces at the prime 2 and should be of independent interest. Our proofs of relations for unstable operations rely on Atiyah's Real K-theory and on a convenient mod 2 simplification of 2-adic KO-cohomology. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Fausk-Isaksen/filtered Title: Model structures on pro-categories Authors: Halvard Fausk, Daniel C. Isaksen E-mail: fausk@math.uio.no, isaksen@math.wayne.edu AMS Classification: 55U35 Primary ; Secondary 55P91, 18G55 Abstract: We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for $G$-spaces, where $G$ is a pro-finite group. The class of weak equivalences is an approximation to the class of underlying weak equivalences. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Fausk-Isaksen/t-model Title: T-model structures Authors: Halvard Fausk and Daniel C. Isaksen E-mail: fausk@math.uio.no, isaksen@math.wayne.edu AMS Classification: Primary 55P42; Secondary 18E30, 55U35 Abstract: For every stable model category $\mathcal{M}$ with a certain extra structure, we produce an associated model structure on the pro-category pro-$\mathcal{M}$ and a spectral sequence, analogous to the Atiyah-Hirzebruch spectral sequence, with reasonably good convergence properties for computing in the homotopy category of pro-$\mathcal{M}$. Our motivating example is the category of pro-spectra. The extra structure referred to above is a t-model structure. This is a rigidification of the usual notion of a t-structure on a triangulated category. A t-model structure is a proper simplicial stable model category $\mathcal{M}$ with a t-structure on its homotopy category together with an additional factorization axiom. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Neusel/piotr Connected Hopf algebras with Dixmier bases and infinite primary decomposition Mara D. Neusel Mara.D.Neusel@ttu.edu Abstract: In this paper we study the existence of invariant primary decompositions for algebras and modules over Hopf algebras. This is an update of the previous preprint of Neusel-Wisniewski of the same title. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Neusel-Sezer/noether The Noether map AUTHORS: Mara D. Neusel (Texas Tech University), M\"ufit Sezer (Bo\u gazici \"Universitesi) EMAILS: mara.d.neusel@ttu.edu mufit.sezer@boun.edu.tr ABSTRACT: Let $\rho: G\hra GL(n\/,\ \F)$ 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. Furthermore, we show that the Noether map is surjective, i.e., its image integrally closed, if $V=\F^n$ is a projective $\F G$-module. Moreover, we show that the converse of this statement is true if $G$ is a $p$-group and $\F$ has characteristic $p$, or if $\rho$ is a permutation representation. We apply these results and obtain upper bounds on the Noether number and the Cohen-Macaulay defect of $\F[V]^G$. We illustrate our results with several examples. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Siebenmann/Schoen-02Sept2005 The Osgood-Schoenflies Theorem Revisited by Laurent Siebenmann Math'ematique, B^at. 425, Universit'e de Paris-Sud, 91405-Orsay, France http://topo.math.u-psud.fr/~lcs/contact This retrospective article presents an elementary, and hopefully direct and clear, geo- metric proof of what is usually called the (classical planar) Schoenflies Theorem; it is stated as (ST) in x4 below _ with mention of its early history, including W.F. Osgood's rarely cited contributions. This (ST) is essentially the fact _ surprising in view of known fractal curves _ that every compact subset of the cartesian plane R2 that is homeomorphic to the circle S1, is necessarily the frontier in R2 of a set homeomorphic to the 2-disk. Beware that the `Generalized Schoenflies theorem' of B. Mazur [Maz] and M. Brown [Brow1] _ proved five decades later and valid in all dimensions _ does not imply (ST) since it assumes a condition of flatness (or local flatness [Brow2]). ---------------------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.