Subject: new Hopf listings From: Mark Hovey Date: 01 Jan 2007 11:45:05 -0500 There are 7 new papers this time, from Castellana-Crespo-Scherer, Clement-Scherer, Colman, Maltsiniotis, Matthey-Pitsch-Scherer, Nakagawa, and Ruiz. Mark Hovey New papers appearing on hopf between 12/7/06 and 1/1/07 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Castellana-Crespo-Scherer/covers Title: On the cohomology of highly connected covers of finite complexes Authors: Natalia Castellana, Juan A. Crespo, and Jerome Scherer Abstract: Relying on the computation of the Andre-Quillen homology groups for unstable Hopf algebras, we prove that the mod p cohomology of the n-connected cover of a finite H-space is always finitely generated as algebra over the Steenrod algebra. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Clement-Scherer/exponent Title: Homology exponents for H-spaces Authors: Alain Clement and Jerome Scherer Abstract: We say that a space X admits a homology exponent if there exists an exponent for the torsion subgroup of the integral homology. Our main result states that if an H-space of finite type admits a homology exponent, then either it is, up to 2-completion, a product of spaces of the form BZ/2^r, S1, K(Z,2), and K(Z,3), or it has infinitely many non-trivial homotopy groups and k-invariants. We then show with the same methods that simply connected H-spaces whose mod 2 cohomology is finitely generated as an algebra over the Steenrod algebra do not have homology exponents, except products of mod 2 finite H-spaces with copies of K(Z,2) and K(Z,3). 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Colman/ColmanHTG Title of Paper: On the homotopy type of Lie groupoids Author: Hellen Colman Address of Author: Department of Mathematics, Wilbur Wright College, 4300 N. Narragansett Avenue, Chicago, IL 60634 USA Text of Abstract: We propose a notion of groupoid homotopy for generalized maps. This notion of groupoid homotopy generalizes the notions of natural transformation and strict homotopy for functors. The groupoid homotopy type of a Lie groupoid is shown to be invariant under Morita equivalence. As an application we consider orbifolds as groupoids and study the orbifold homotopy between orbifold maps induced by the groupoid homotopy. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Maltsiniotis/adjquill Title: Le theoreme de Quillen, d'adjonction des foncteurs derives, revisite Author: Georges MALTSINIOTIS English Translation: math.AT/0611952 Address: Université Paris 7 Denis Diderot Case Postale 7012 2, place Jussieu F-75251 PARIS CEDEX 05 Abstract: The aim of this paper is to present a very simple original, purely formal, proof of Quillen's adjunction theorem for derived functors, and of some more recent variations and generalizations of this theorem. This is obtained by proving an abstract adjunction theorem for "absolute" derived functors. In contrast with all known proofs, the explicit construction of the derived functors is not used. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Matthey-Pitsch-Scherer/Blochlift Title: Generalized orientations and the Bloch invariant Authors: Michel Matthey, Wolfgang Pitsch, and Jerome Scherer Abstract: For compact hyperbolic 3-manifolds we lift the Bloch invariant defined by Neumann and Yang to an integral class in K_3(C). Applying the Borel and the Bloch regulators, one gets back the volume and the Chern-Simons invariant of the manifold. We also discuss the non-compact case, in which there appears a Z/2-ambiguity. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Nakagawa/cohomologyE8 Title: The integral cohomology ring of E_8/T1 E_7 Author: Masaki Nakagawa Address of author: Department of General Education, Takamatsu National College of Technology, 355 Chokushi-cho, Takamatsu, 761-8058, Japan Abstract: The generalized flag manifolds are homogeneous spaces of the form G/C, where G is a compact connected Lie group and C is the centralizer of a torus in G. These homogeneous spaces play an important role in algebraic topology, algebraic geometry and differential geometry. In this paper, using the Borel presentation and a method due to Toda, we determine the integral cohomology ring of a certain generalized flag manifold which is a quotient space of the exceptional Lie group E8. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Ruiz/ar-gl-rv Title: Exotic normal fusion subsystems of General Linear Groups. Author: Albert Ruiz Institution: Departament de Matematiques, Universitat Autonoma de Barcelona, 08193 Cerdanyola del Valles, Spain. Abstract: We classify the saturated fusion subsystems of index prime to $p$ of the general linear group over $F_q$ over a Sylow $p$-subgroup, where $q$ is a prime power prime to an odd prime $p$. In this classification we get some of the exotic $p$-local finite groups discovered by C. Broto and J. Moller as saturated fusion subsystems of the general linear 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://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.