Subject: new Hopf listings Date: 11 Jul 2003 05:32:36 -0400 From: Mark Hovey Reply-To: mhovey@wesleyan.edu To: dmd1@lehigh.edu 6 new papers this time, from Baas-Dundas-Rognes (an update), Richter, Sinha, Strickland, and (Jim) Turner (2), Mark Hovey New papers appearing on hopf between 6/18/03 and 7/11/03 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Baas-Dundas-Rognes/segal60 Title of Paper: Two-vector bundles and forms of elliptic cohomology Authors: Nils A. Baas, Bjorn I. Dundas and John Rognes Email address of Authors: baas@math.ntnu.no, dundas@math.ntnu.no and rognes@math.uio.no In this paper we define 2-vector bundles as suitable bundles of 2-vector spaces over a base space, and compare the resulting 2-K-theory with the algebraic K-theory spectrum K(V) of the 2-category of 2-vector spaces, as well as the algebraic K-theory spectrum K(ku) of the connective topological K-theory spectrum ku. We explain how K(ku) detects v_2-periodic phenomena in stable homotopy theory, and as such is a form of elliptic cohomology. (This is an new version of a paper previously on Hopf). 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Richter/Richter-Lambda-EHP Title: Lambda algebra unstable composition products and the Lambda EHP sequence Author: William Richter AMS Classification numbers: 55T15, 55Q40, 55Q25 Address: Math Department, Northwestern University, Evanston IL 6020 Email: richter@math.nwu.edu Abstract: Simple combinatorial proofs are given of Lambda algebra results, mostly due to Priddy & the 6 authors, but also the ``Adams filtration better'' unstable Lambda products of Wang, Mahowald and Singer: Lambda^{s,t}(n) @ Lambda(n+t ) ---> Lambda(n) which imply the folklore Lambda EHP sequence Lambda(n) >-E--> Lambda(n+1) -H-->> Lambda(2n+1) The 6 authors proved Lambda(n) is a chain complex, but not that H is a chain map. A careful reader could deduce a proof from the papers of Wang, Mahowald and Singer, but Singer, who best stated the formulas, gave no proofs. New results: combinatorial proofs of the Lambda admissible monomial basis; the differential d is well-defined. The paper should be accessible to geometers interested in forthcoming applications with Mahowald on 3-cell Poincare complexes. Perhaps the Lambda algebra is undergoing a Renaissance, as 2 young people, Mark Behrens and Mizuho Hikida are doing interesting new work in it. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Sinha/compactify Title: Manifold theoretic compactifications of configuration spaces. Author: Dev P. Sinha AMS Class: 55R80; 32J05 LANL ID: math.GT/0306385 Addresses: Departments of Mathematics, University of Oregoni, Eugene, OR 97403 Email: dps@math.uoregon.edu Abstract: We present new definitions for and give a comprehensive treatment of the canonical compactification of configuration spaces due to Fulton-MacPherson and Axelrod-Singer in the setting of smooth manifolds, as well as a simplicial variant of this compactification. Our constructions are elementary and give simple global coordinates for the compactified configuration space of a general manifold embedded in Euclidean space. We stratify the canonical compactification, identifying the diffeomorphism types of the strata in terms of spaces of configurations in the tangent bundle, and give completely explicit local coordinates around the strata as needed to define a manifold with corners. We analyze the quotient map from the canonical to the simplicial compactification, showing it is a homotopy equivalence. We define projection maps and diagonal maps, which for the simplicial variant satisfy cosimplicial identities. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Strickland/axsurv Axiomatic stable homotopy--a survey by N. P. Strickland We survey various approaches to axiomatic stable homotopy theory, with examples including derived categories, categories of (possibly equivariant or localized) spectra, and stable categories of modular representations of finite groups. We focus mainly on representability theorems, localisation, Bousfield classes, and nilpotence. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Turner/finite On simplicial commutative algebras with finite Andre-Quillen homology by James M. Turner L. Avramov, following D. Quillen, posed a conjecture to the effect that if $R \to A$ is a homomorphism of Noetherian rings then the Andr\'e-Quillen homology on the category of A-modules satisfies: $D_{s}(A|R;-) = 0$ for $s\gg 0$ implies $D_{s}(A|R;-) = 0$ for s>2. In an earlier paper, the author posed an extended version of this conjecture which considered A to be a simplicial commutative R-algebra with Noetherian homotopy such that the characteristic of $\pi_{0}A$ is non-zero. In addition, a homotopy characterization of such algebras was described. The main goal of this paper is to develop a strategy for establishing this extended conjecture and provide a complete proof when R is Cohen-Macaulay of characteristic 2. Note: this paper replaces "Nilpotency in the homotopy of simplicial commutative algebras". 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Turner/Gorenstein Characterizing Simplicial Commutative Algebras with Vanishing Andr'e-Quillen Homology by James M. Turner The use of homological and homotopical devices, such as Tor and Andr\'e-Quillen homology, have found substantial use in characterizing commutative algebras. The primary category setting has been differentially graded algebras and modules, but recently simplicial categories have also proved to be useful settings. In this paper, we take this point of view up a notch by extending some recent uses of homological algebra in characterizing Noetherian commutative algebras to characterizing simplicial commutative algebras having finite Noetherian homotopy through the use of simplicial homotopy theory. These characterizations involve extending the notions of locally complete intersections and locally Gorenstein algebras to the simplicial homotopy setting. ---------------------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 can also use ftp, explained below. The largest archive of math preprints is at http://xxx.lanl.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 xxx, send e-mail to math@xxx.lanl.gov with subject line "subscribe" (without quotes), and with the body of the message "add AT" (without quotes). You can also access Hopf through ftp. Ftp to hopf.math.purdue.edu, and login as ftp. Then cd to pub. Files are organized by author name, so papers by me are in pub/Hovey. If you want to download a file using ftp, you must type binary before you type get . To put a paper of yours on the archive, go to http://hopf.math.purdue.edu and use the web form. You can also use anonymous ftp as above. First cd to /pub/incoming. Transfer the dvi file using binary, by first typing binary then put You should also transfer 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@math.purdue.edu telling him what you have uploaded. I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive.