Subject: new Hopf listings From: Mark Hovey Date: 08 Feb 2006 09:45:32 -0500 There are 4 new papers this time, from Biedermann-Chorny-Roendigs, Bubenik-Worytkiewicz, DavisD-Theriault, and Fresse. Mark Hovey New papers appearing on hopf between 1/4/06 and 2/8/06 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Biedermann-Chorny-Roendigs/biedermann-chorny-roendigs Title: Goodwillie's calculus and model categories Author(s): Georg Biedermann, Boris Chorny, Oliver Roendigs Author's e-mail address: gbiederm@uwo.ca, chorny@math.ethz.ch, oroendig@math.uni-bielefeld.de Abstract: The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure. In this paper we construct various localizations of the projective model structure and also give a variant for functors from simplicial sets to spectra. We apply these model categories in the study of calculus of functors, namely for classification of polynomial and homogeneous functors. Finally we show that the $n$-th derivative induces a Quillen map between the $n$-homogeneous model structure on small functors from pointed simplicial sets to spectra and the category of spectra with $\Sigma_n$-action. We consider also a finitary version of the $n$-homogeneous model structure and the $n$-homogeneous model structure on functors from pointed finite simplicial sets to spectra. In these two cases the above Quillen map becomes a Quillen equivalence. This improves the classification of finitary homogeneous functors by T. G. Goodwillie. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Bubenik-Worytkiewicz/lps title: A model category for local po-spaces author: Peter Bubenik email: p.bubenik@csuohio.edu author: Krzysztof Worytkiewicz email: kworytki@uwo.ca to appear in: Homology, Homotopy and Applications abstract: Locally partial-ordered spaces (local po-spaces) have been used to model concurrent systems. We provide equivalences for these spaces by constructing a model category containing the category of local po-spaces. We show the category of simplicial presheaves on local po-spaces can be given Jardine's model structure, in which we identify the weak equivalences between local po-spaces. In the process we give an equivalence between the category of sheaves on a local po-space and the category of {\'e}tale bundles over a local po-space. Finally we describe a localization that should provide a good framework for studying concurrent systems. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/DavisD-Theriault/theri6 Odd-primary homotopy exponents of compact simple Lie groups Donald M. Davis and Stephen D. Theriault dmd1@lehigh.edu s.theriault@maths.abdn.ac.uk We note that a recent result of the second author yields upper bounds for odd-primary homotopy exponents of compact simple Lie groups which are often quite close to the lower bounds obtained from v1-periodic homotopy theory. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Fresse/Bar-StructureUniqueness Title: The bar construction of an $E$-infinity algebra Author: Benoit Fresse E-mail: Benoit.Fresse@math.univ-lille1.fr Abstract: We consider the classical reduced bar construction of associative algebras B(A). If the product of A is commutative, then B(A) can be equipped with the classical shuffle product, so that B(A) is still a commutative algebra. This assertion can be generalized for algebras which are commutative up to homotopy. Namely, one observes that the bar construction of an E-infinite algebra B(A) can be endowed with the structure of an E-infinite algebra. The purpose of this article is to give an existence and uniqueness theorem for this claim. We would like to insist on the uniqueness property: our statement makes the construction of $E$-infinite structures easier and more flexible. Therefore, the proof of our existence theorem differs from other constructions of the literature. In addition, the uniqueness property allows to give easily a homotopy interpretation of the bar construction. ---------------------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.