Subject: new Hopf listings From: Mark Hovey Date: 05 Sep 2005 08:55:45 -0400 There are 6 new papers this time, from Bergner (2), Chebolu, Hornbostel-Naumann, Lueck-Reich, and Notbohm. Mark Hovey New papers appearing on hopf between 8/4/05 and 9/5/05 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Bergner/MultiSort Title: Rigidification of algebras over multi-sorted algebraic theories Author: Julia E. Bergner Author's e-mail address: bergnerj@member.ams.org AMS Classification: 18C10, 18G30, 18E35, 55P48 arXiv submission number: math.AT/0508152 Author's address: Kansas State University 138 Cardwell Hall Manhattan, KS 66506 Abstract: We define the notion of a multi-sorted algebraic theory, which is a generalization of an algebraic theory in which the objects are of different ``sorts." We prove a rigidification result for simplicial algebras over these theories, showing that there is a Quillen equivalence between a model category structure on the category of strict algebras over a multi-sorted theory and an appropriate model category structure on the category of functors from a multi-sorted theory to the category of simplicial sets. In the latter model structure, the fibrant objects are homotopy algebras over that theory. Our two main examples of strict algebras are operads in the category of simplicial sets and simplicial categories with a given set of objects. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Bergner/SimplicialMonoids Title: Simplicial monoids and Segal categories Author: Julia E. Bergner Author's e-mail address: bergnerj@member.ams.org AMS Classification: 18G30, 18E35, 18C10, 55U40 arXiv submission number: math.AT/0508416 Author's address: Kansas State University 138 Cardwell Hall Manhattan, KS 66506 Abstract: Much research has been done on structures equivalent to topological or simplicial groups. In this paper, we consider instead simplicial monoids. In particular, we show that the usual model category structure on the category of simplicial monoids is Quillen equivalent to an appropriate model category structure on the category of simplicial spaces with a single point in degree zero. In this second model structure, the fibrant objects are reduced Segal categories. We then generalize the proof to relate simplicial categories with a fixed object set to Segal categories with the same fixed set in degree zero. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Chebolu/chromatic Title: Refining thick subcategory theorems Author: Sunil Chebolu Email address: schebolu@uwo.ca AMS classification numbers: Primary: 55P42, 18G55, 19A99 Address: Department of Mathematics, University of Western Ontario, London, ON, N6A 5B7 Abstract: We use a $K$-theory recipe of Thomason to obtain classifications of triangulated subcategories via refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classification of the triangulated subcategories of perfect complexes over some noetherian rings. In the homotopy category of spectra we obtain only a partial classification of the triangulated subcategories of the finite $p$-local spectra. We use this partial classification to study the lattice of triangulated subcategories. This study gives some new evidence to a conjecture of Adams that the thick subcategory $\C_2$ can be generated by iterated cofiberings of the Smith-Toda complex. We also discuss various consequences of these classifications theorems. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Hornbostel-Naumann/f-invofbeta Title: Beta-elements and divided congruences Authors: Jens Hornbostel, Niko Naumann e-mail: jens.hornbostel@mathematik.uni-regensburg.de, niko.naumann@mathematik.uni-regensburg.de Abstract: The f-invariant is an injective homomorphism from the 2-line of the Adams-Novikov spectral sequence to a group which is closely related to divided congruences of elliptic modular forms. We compute the f-invariant for two infinite families of beta-elements and explain the relation of the arithmetic of divided congruences with the Kervaire invariant one problem. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Lueck-Reich/lueck+reich0805 Title of Paper: Detecting K-theory by cyclic homology Author(s): Wolfgang Lueck and Holger Reich AMS Classification number: 19D55 xxx_archive: math.KT/0509002 Addresses of Authors: Mathematisches Institut Westfaelische Wilhelms-Universitaet Einsteinstr. 62 48149 Muenster Germany Email address of Authors: lueck@math.uni-muensetr.de reichh@math.uni-muenster.de Text of Abstract (try for 20 lines or less) We discuss which part of the rationalized algebraic K-theory of a group ring is detected via trace maps to Hochschild homology, cyclic homology, periodic cyclic or negative cyclic homology. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Notbohm/cmcomplex Title: Cohen-Macaulay and Gorenstein complexes from a topological point of view Author: Dietrich Notbohm AMS Classification numbers: 13F55, 55R35 Address of Author: Dept. of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, England Email address: dn8@mcs.le.ac.uk Abstract: The main invariant to study the combinatorics of a simplicial complex $K$ is the associated face ring or Stanley-Reisner algebra. Reisner respectively Stanley explained in which sense Cohen-Macaulay and Gorenstein properties of the face ring are reflected by geometric and/or combinatoric properties of the simplicial complex. We give a new proof for these result by homotopy theoretic methods and constructions. Our approach is based on ideas used very successfully in the analysis of the homotopy theory of classifying spaces. ---------------------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.