5 new papers this month, from Basterra-Mandell, BrownR, Diaz-Ruiz-Viruel, Dugger-Isaksen, and Kuhn. Mark Hovey New papers appearing on hopf between 7/2/04 and 8/7/04 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Basterra-Mandell/Basterra-Mandell-stability Title: Homology and Cohomology of E-infinity Ring Spectra Authors: Maria Basterra Department of Mathematics, University of New Hampshire, Durham, NH basterra@math.unh.edu Michael A. Mandell Department of Mathematics, University of Chicago, Chicago, IL mandell@math.uchicago.edu AMS Subject class: Primary 55P43; Secondary 55P48, 55U35 Abstract: We show that every homology or cohomology theory on a category of E-infinity ring spectra is Topological Andr'e-Quillen homology or cohomology with appropriate coefficients. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/BrownR/IMA-talk Author: Ronald Brown Author's e-mail address: r.brown@bangor.ac.uk Author's web page: http://www.bangor.ac.uk/~mas010 Author's mailing address: Professor Emeritus R. Brown, Department of Mathematics, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom AMS classification number: 18D05,18D15,18G50,55P15,55U40,57M07 arXive submission number: math.AT/0407275 Abstract: We sketch the background to a book with the title `Nonabelian algebraic topology' being written under support of a Leverhulme Emeritus Fellowship (2002-2004) by the speaker and Rafael Sivera (Valencia). The aim is to give in one place a full account of work by R. Brown and P.J. Higgins and others since the 1970s which defined and applied crossed complexes and cubical higher homotopy groupoids to local-to-global problems and homotopy classification of maps. This yields a distinctive account of that part of algebraic topology which lies between homology theory and homotopy theory, in which the fundamental group and its actions plays an essential role, and which allows for nonabelian calculations in dimension 2. This is an extended account of a short presentation with this title given at the Minneapolis IMA Workshop on `$n$-categories: foundations and applications', June 7-18, 2004, organised by John Baez and Peter May. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Diaz-Ruiz-Viruel/drv Title: All p-local finite groups of rank two for odd prime p Authors: Antonio Diaz, Albert Ruiz, Antonio Viruel Author's e-mail address: adiaz@agt.cie.uma.es, Albert.Ruiz@uab.es, viruel@agt.cie.uma.es ArXive submission number: math.AT/0407324 Abstract: In this paper we give a classification of the rank two p-local finite groups for odd p. This study requires the analysis of the possible saturated fusion systems in terms of the outer automorphism group and the proper F-radical subgroups. Also, for each case in the classification, either we give a finite group with the corresponding fusion system or we check that it corresponds to an exotic p-local finite group, getting some new examples of these for p = 3. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Dugger-Isaksen/ksumDI Algebraic K-theory and sums-of-squares formulas Daniel Dugger and Daniel C. Isaksen Email: ddugger@math.uoregon.edu and isaksen@math.wayne.edu Addresses: Daniel Dugger Department of Mathematics University of Oregon Eugene, OR 97403 Daniel C. Isaksen Department of Mathematics Wayne State University Detroit, MI 48202 Abstract: We prove a result about the non-existence of certain sums-of-squares formulas over a field. This generalizes an old theorem which used topological K-theory to produce obstruction conditions when the field is the real numbers. Our result applies to arbitrary fields not of characteristic 2, making use of algebraic K-theory in place of topological K-theory. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Kuhn/homologyiso Title: Mapping spaces and homology isomorphisms Author: Nicholas J. Kuhn AMS classification numbers: 55P35, 55N20, 55P42 arXiv no.: math.AT/0407146 address: University of Virginia, Charlottesville, VA USA email: njk4x@virginia.edu Abstract: Let Map(K,X) denote the space of pointed continuous maps from a finite cell complex K to a space X. Let E_* be a generalized homology theory. We use Goodwillie calculus methods to prove that under suitable conditions on K and X, Map(K, X) will send an E_*--isomorphism in either variable to a map that is monic in E_* homology. Interesting examples arise by letting E_* be K--theory, K be a sphere, and the map in the X variable be an exotic unstable Adams map between Moore spaces. ---------------