Subject: new Hopf listings From: Mark Hovey Date: 04 Jan 2006 11:58:43 -0500 There are 8 new papers this time, from Arone-Lesh, BrownR, Gutierrez, Inoue-Yagita, Klein-Williams, Korbas, Lockridge, and Ziemianski Mark Hovey New papers appearing on hopf between 11/11/05 and 1/4/06 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Arone-Lesh/arone-lesh-press Title: Filtered spectra arising from permutative categories Authors: Gregory Arone University of Virginia Kathryn Lesh Union College Abstract: Given a special Gamma-category C satisfying some mild hypotheses, we construct a sequence of spectra interpolating between the spectrum associated to C and the Eilenberg-Mac Lane spectrum HZ. Examples of categories to which our construction applies are: the category of finite sets, the category of finite-dimensional vector spaces, and the category of finitely-generated free modules over a reasonable ring. In the case of finite sets, our construction recovers the filtration of HZ by symmetric powers of the sphere spectrum. In the case of finite-dimensional complex vector spaces, we obtain an apparently new sequence of spectra, A_{m}, that interpolate between bu and HZ. We think of A_{m} as a ``bu-analogue'' of the m'th symmetric power of the sphere and describe far-reaching formal similarities between the two sequences of spectra. For instance, in both cases the m'th subquotient is contractible unless m is a power of a prime, and in v_{k}-periodic homotopy the filtration has only k+2 nontrivial terms. There is an intriguing relationship between the bu-analogues of symmetric powers and Weiss's orthogonal calculus, parallel to the not yet completely understood relationship between the symmetric powers of spheres and the Goodwillie calculus of homotopy functors. We conjecture that the sequence {A_{m}}, when rewritten in a suitable chain complex form, gives rise to a minimal projective resolution of the connected cover of $bu$. This conjecture is the bu-analogue of a theorem of Kuhn and Priddy about the symmetric power filtration. The calculus of functors provides substantial supporting evidence for the conjecture. This is a revision of a preprint previously submitted to Hopf. The paper has been accepted for publication in Journal für die reine und angewandte Mathematik (Crelle's Journal). 2. http://hopf.math.purdue.edu/cgi-bin/generate?/BrownR/PB-jordan Title: Groupoids, the Phragmen-Brouwer Property, and the Jordan Curve Theorem Author: Ronald Brown Author's e-mail address: r.brown at bangor.ac.uk Author's mailing address: Mathematics Department, School of Informatics, University of Wales, Bangor, Gwynedd LL57 1UT, UK Author's web site: www.bangor.ac.uk/r.brown Preprint: University of Wales Math Preprint 06.01 Abstract: We publicise a proof of the Jordan Curve Theorem which relates it to the Phragmen-Brouwer Property, and whose proof uses the van Kampen theorem for the fundamental groupoid on a set of base points. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Gutierrez/hlems Homological localizations of Eilenberg-Mac Lane spectra Javier J. Guti\'errez We discuss the Bousfield localization $L_E X$ for any spectrum $E$ and any $HR$-module $X$, where $R$ is a ring with unit. Due to the splitting property of $HR$-modules, it is enough to study the localization of Eilenberg--Mac\,Lane spectra. Using general results about stable $f$-localizations, we give a method to compute the localization of an Eilenberg--Mac\,Lane spectrum $L_E HG$ for any spectrum $E$ and any abelian group $G$. We describe $L_E HG$ explicitly when $G$ is one of the following: finitely generated abelian groups, $p$-adic integers, Pr\"ufer groups, and subrings of the rationals. The results depend basically on the $E$-acyclicity patterns of the spectrum $H\Q$ and the spectrum $H\Z/p$ for each prime $p$. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Inoue-Yagita/bpso Title: The complex cobordism of BSOn Authors: K.Inoue and N.Yagita Abstract: In this paper, we compute MU(BSO(2n)) and show that it is generated as an MU-algebra by Conner-Floyd Chern classes and one 2n-dimensional element. For the case BO(m) are still studied by W.S.Wilson. We get the result by using (equivariant) stratification methods introduced to compute Chow rings by Guillot, Molina, Vessozi and Vistoli. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Klein-Williams/int-theoryI Homotopical intersection theory, I. by John R. Klein and E. Bruce Williams Abstract: We give a new approach to intersection theory. Our ``cycles'' are closed manifolds mapping into compact manifolds and our ``intersections'' are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems resemble those of Hatcher and Quinn. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Korbas/cuplength Title: Bounds for the cup-length of Poincare spaces and their applications Author: Julius Korbas AMS Classification numbers: Primary: 57N65; 55M30 Secondary: 53C30 Author's addresses: Department of Algebra, Geometry, and Mathematical Education, Faculty of Mathematics, Physics, and Informatics, Comenius University, Mlynska dolina, SK-842 48 Bratislava 4, Slovakia or Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, SK-814 73 Bratislava 1, Slovakia Abstract: Our main result offers a new (quite systematic) way of deriving bounds for the cup-length of Poincare spaces over fields; we outline a general research program based on this result. For the oriented Grassmann manifolds, already a limited realization of the program leads, in many cases, to the exact values of the cup-length and to interesting information on the Lyusternik-Shnirel'man category. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Lockridge/gh Title: The generating hypothesis in the derived category of R-modules. Author: Keir H. Lockridge Abstract: In this paper, we prove a version of Freyd's generating hypothesis for triangulated categories: if D is a cocomplete triangulated category and S is an object in D whose endomorphism ring is graded commutative and concentrated in degree zero, then S generates (in the sense of Freyd) the thick subcategory determined by S if and only if the endomorphism ring of S is von Neumann regular. As a corollary, we obtain that the generating hypothesis is true in the derived category of a commutative ring R if and only if R is von Neumann regular. We also investigate alternative formulations of the generating hypothesis in the derived category. Finally, we give a characterization of the Noetherian stable homotopy categories in which the generating hypothesis is true. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/Ziemianski/SpinHtpReps TITLE: Homotopy representations of Spin(7) and SO(7) at prime 2 AUTHOR: Krzysztof Ziemianski ADDRESS: Faculty of Mathematics, Informatics and Mechanics Warsaw University Banacha 2 02-097 Warszawa POLAND ABSTRACT: A homotopy (complex) representation of a compact connected Lie group L at prime p is a map from BL into the p-completion of the classifying space of the unitary group. In this paper we give a partial classification of homotopy representations of SO(7) and Spin(7) at prime 2. Motiviation for considering this problem is twofold: first, one may hope that it would help to understand maps between classifying spaces. Secondly, construction of a homotopy representation of Spin(7) is a crucial step in the construction of a faithful representation of the 2-compact group DI(4). ---------------------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.