Subject: new Hopf listings From: Mark Hovey Date: 04 Dec 1998 05:43:45 -0500 The math department Unix system at Wesleyan was hacked into and had to be totally reinstalled. My web pages are thus down, and may well continue to be down for another week or so. In any case, I anticipate the URL of my home page will change, hopefully to something more reasonable. Nine new papers this time. Mark Hovey New papers uploaded to hopf between 11/7/98 and 12/3/98: 1. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Adem-Karoubi/AK C.R. Acad. Sci. Paris, t. 326 ,Série I, p. 13­17 (1998) Algèbre/Algebra (Topologie algébrique/Algebraic Topology) PERIODIC CYCLIC COHOMOLOGY OF GROUP RINGS Alejandro ADEM et Max KAROUBI A.A. : Mathematics Department, University of Wisconsin, Van Vleck Hall Madison, WI 53706, ETATS­UNIS ; e.mail : adem@math.wisc.edu M. K. : Université Paris 7 ­ Mathématiques, UMR 9994 du CNRS 2, place Jussieu 75251 Paris Cedex 05, FRANCE ; e.mail : karoubi@math.jussieu.fr Abstract. We generalize previous results ([2], [3], [4], etc.) relative to the cyclic homology and cohomology of the group algebra of G. In many cases, we express them in terms of the (co)homology of the discrete groups Z(u) = Z(u)/C(u), where runs through the set of conjugacy classes of G and where Z(u) (resp. C(u)) denotes the centralizer of u (resp. the cyclic group generated by u). 2. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Berrick/berrictp The plus-construction as a localization A J Berrick Department of Mathematics National University of Singapore Kent Ridge 119260 Singapore berrick@math.nus.edu.sg To appear in Algebraic K-Theory and its Applications, Proc Symp ICTP, Trieste, World Scientific (Singapore). AMS Classification numbers. 16S34, 18E35, 19-02, 19D06, 20H25, 55P60 Abstract . An initial survey contrasts two points of view in the historical development of the theory of localization. The first, starting with inversion of elements in a ring, leads to quotient categories and indirectly to the Q-construction. The second considers idempotent functors. This leads to the Berrick-Casacuberta description of the plus-construction on X as the idempotent functor that is nullification of X with respect to an acyclic space W. Focus on the case X = BGLR produces new results, including the classification of perfect normal subgroups of GLR. When R is a group ring AG, links are obtained between these perfect normal subgroups and the A-representability of the group G. A final section studies the relationship between the plus-construction on BGLR and acyclicity of the space W. This prompts some general questions on the K-theory of rings. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Fresse/SimpAlgOp Title: On the homotopy of simplicial algebras over an operad Author: Benoit Fresse Address: Laboratoire J.A.Dieudonne Universite de Nice-Sophia-Antipolis et CNRS Parc Valrose F-06108 Nice Cedex 02 E-mail: fresse@math.unice.fr Abstract: According to a result of H. Cartan, the homotopy of a simplicial commutative algebra is equipped with divided power operations. In this article, we show how to extend this result to other kinds of algebras. For instance, we prove that the homotopy of a simplicial Lie algebra is equipped with the structure of a restricted Lie algebra. Comments: This article is a revised version of the paper: ``Cartan operations for a simplicial algebra over an operad''. In the former version, the proof of the following claim contains a serious defect. Let $M$ be a representation of the symmetric group. Let $V$ be a simplicial vector space. The transfer $$(M\otimes V^{\otimes n})_{S_n}\,\rightarrow\,(M\otimes V^{\otimes n})^{S_n}$$ is homotopy injective. The new construction does not depend on this property. The paper is to appear in the Transactions of the AMS. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Grieder/geomrepr Title: Geometric Representation Theory and G-Signature Author: Ralph Grieder Math. Sub. Class. 91: Primary 57S25, 20C15, 57R85; Secondary 20F38, 58G10, 11R29. Department of Mathematics, Northwestern University, Evanston, IL 60208 ralph@math.nwu.edu Let G be a finite group. To every smooth G-action on a compact, connected and oriented surface we can associate its data of singular orbits. The set of such data becomes an Abelian group B_G under the G-equivariant connected sum. We will show that the map which sends G to B_G is functorial and carries many features of the representation theory of finite groups. We will prove that B_G consists only of copies of Z and Z/2Z. Furthermore we will show that there is a surjection from the G-equivariant cobordism group of surface diffeomorphisms to B_G. We will define a G-signature which is related to the G-signature of Atiyah and Singer and prove that this new G-signature is injective on the copies of Z in B_G. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Klein/compress1 Embedding, compression and fiberwise homotopy theory. by John R. Klein Wayne State University klein@math.wsu.edu This paper establishes a `Cairns-Hirsch' type result for Poincare embeddings: it gives criteria in the metastable range for a Poincare embedding M x I ---> X x I between n-dimensional Poincare spaces to arise from a Poincare embedding M --> X. This result has quite a few applications. To mention a few: 1) a Poincare embedding theorem for spheres in the middle dimension. 2) a Poincare analogue of Levine's embedding theorem. 3) a Poincare version of the Whitney embedding theorem (settling a question of Levitt) 4) the existence of diagonal Poincare embeddings (in the 1-connected case). Included .eps files: pic1a-comp.eps pic2-comp.eps pic3.eps 6. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Klein/haef Poincare duality embeddings and fiberwise homotopy theory. by John R. Klein Wayne State University klein@math.wsu.edu This paper establishes an embedding theorem for finite complexes mapping to Poincare spaces. The theorem is the Poincare version of the `embedded thickening theorem' of C.T.C Wall. The theorem says that a (2k - n + 2)-connected map f: K^k --> X^n (from a finite complex of dimension k to an n-dimensional Poincare space) is the underlying map of a Poincare embedding, provided also that k < n - 2. This paper will appear in Topology. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Klein/smale Poincare Immersions. by John R. Klein Wayne State University klein@math.wsu.edu This paper establishes a Poincare variant of the fundamental theorem of immersion theory. It has been already accepted for publication in Forum Mathematicum. Given a map f:M^n --> X^n with M and X n-dimensoinal Poincare duality spaces (with or without boundary). One says that f *immerses* if f x id : M x D^j ---> X x D^j is the underlying map of a Poincare embedding for sufficiently large j. Theorem A of this paper says that f immerses if and only if the pullback of the Spivak normal fibration of X is stable fiber homotopy equivalent to the Spivak normal fibration of M. Also included is a new homotopy theoretic proof (using equivariant duality) of the existence and uniqueness theorems for the Spivak fibration. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Klein/survey-apr10 Poincare Duality Spaces by John R. Klein Wayne State University klein@math.wsu.edu This is a survey paper on Poincare spaces. Among the included topics are classification (low dimensional, highly connected), Poincare embeddings, Poincare surgery, the finite H-space problem. This paper will eventually appear in a volume dedicated to C.T.C Wall's 60th Birthday (edited by S. Cappell, A. Ranicki and J. Rosenberg). 9. http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Moyaux/artLBRC4 Title of Paper: Two lower bounds for the relative L.S. category. Author: Pierre-Marie MOYAUX. AMS Classification numbers:55M30, 57R70. Addresse of the author: Pierre-Marie MOYAUX; Universite de Lille 1; U.F.R. de Mathematiques & U.R.A 751 au CNRS; 59655 Villeneuve D'Ascq, France. Email address of the author: moyaux@gat.univ-lille1.fr Included EPS or PS files : none. Text of Abstract: We prove that $ \sigma ^{p+1}cat(X) +1 \leq cat(X,X \times S^{p}) $ and that $e(X,X\times S^{p})=e(X)+1$, where $ \sigma ^{p+1}cat$ is the $ \sigma-$category of Vandembroucq and $e$ is the Toomer invariant. The proof is based on an extension to a relative setting of Milnor's construction of the classifying space of a topological group. ---------------------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://www.cs.wesleyan.edu/Math/Guests/Mark If this doesn't work or is missing a few issues, try http://www.lehigh.edu/~dmd1/public/www-data/algtop.html , which also has the other messages sent to Don's list. To get the papers listed above, point your WWW client (Mosaic, Netscape) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to conference announcements, Purdue seminars, and other math related things on this page as well. 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, 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/pub/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. ------- End of forwarded message -------