Subject: new Hopf listings Date: 02 Jul 2004 14:31:57 -0400 From: Mark Hovey 10 new papers this month, from Bergner, Broto-Moller, Bruner-Rognes, Galvez-Whitehouse, Intermont-Strom, Jardine, Rezk, and YauD (3 papers). Mark Hovey New papers appearing on hopf between 6/2/04 and 7/2/04 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Bergner/SimplicialCategoryMC Title: A model category structure on the category of simplicial categories Author: Julia E. Bergner Author's e-mail address: jbergner@nd.edu AMS Classification: 18G55, 18D20 arXiv submission number: math.AT/0406507 Author's address: Department of Mathematics University of Notre Dame Notre Dame, IN 46556 Abstract: In this paper we put a cofibrantly generated model category structure on the category of small simplicial categories. The weak equivalences are a simplicial analogue of the notion of equivalence of categories. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Broto-Moller/Chev Title: Finite Chevalley versions of p-compact groups Authors: Carles Broto, Jesper M. Moller Author's e-mail address: broto@mat.uab.es moller@math.ku.dk Address: Carles Broto Departament de Matematiques, Universitat Autonoma de Barcelona, 08193 Bellaterra, Spain Address: Jesper M. Moller Matematisk Institut Universitetsparken 5 DK-2100 Copenhagen Denmark AMS class: 55R35, 55P15, 55P10 Abstract: We describe the spaces of homotopy fixed points of unstable Adams operations acting on p-compact groups and also of unstable Adams operations twisted with a finite order automorphism of the p-compact group. We obtain new exotic p-local finite groups. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Bruner-Rognes/bruner Title: Leibniz Formulas for Cyclic Homotopy Fixed Point Spectra Authors: Robert R. Bruner and John Rognes MSC-class: 19D55, 55P43, 55P91, 55S12, 55T05. ArXiv ID: math.AT/0406081 Addresses: Robert R. Bruner Department of Mathematics Wayne State University Detroit, Michigan 48067 USA rrb@math.wayne.edu John Rognes Department of Mathematics University of Oslo Box 1053, Blindern NO-0316 Oslo Norway rognes@math.uio.no Abstract: We analyze the homotopy fixed point spectrum of a circle-equivariant commutative S-algebra R in homological terms. There is a homological homotopy fixed point spectral sequence that converges conditionally to the continuous homology of the homotopy fixed point spectrum. We show that there are Dyer-Lashof operations Q^i acting on this algebra spectral sequence, and that its differentials are completely determined by those originating on the vertical axis. More surprisingly, we show that for each class x in the E^{2r}-term of the spectral sequence there are 2r other classes in the E^{2r}-term (obtained mostly by Dyer-Lashof operations on x) that are infinite cycles, i.e., survive to the E^infty-term. We apply this to completely determine the differentials in the homological homotopy fixed point spectral sequences for the topological Hochschild homology spectra R = THH(B) of many S-algebras, including B = MU, BP, ku, ko and tmf. Similar results apply for all finite subgroups of the circle, and for the Tate- and homotopy orbit spectra. This work is part of a homological approach to calculating topological cyclic homology and algebraic K-theory of commutative S-algebras. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Galvez-Whitehouse/centres Title: Infinite Sums of Adams Operations and Cobordism Authors: Imma Galvez, Sarah Whitehouse E-mail: i.galvezicarrillo@londonmet.ac.uk, s.whitehouse@sheffield.ac.uk Addresses: Computing, Communications Technology and Mathematics, London Metropolitan University, Holloway Road, London N7 8DB, UK. Pure Mathematics, University of Sheffield, Sheffield S3 7RH, UK. Included ps or eps files: centrediag1.ps, centrediag2.ps AMS classification number: Primary: 55S25; Secondary: 55N22, 19L41. Abstract: In recent work by Clarke, Crossley and the second author, various algebras of stable degree zero operations in p-local K-theory were described explicitly. The elements are certain infinite sums of Adams operations. Here we show how to make sense of the same expressions for p-local cobordism and for BP, thus identifying the "Adams subalgebra" of the algebras of operations. We prove that the Adams subalgebra is the centre of the ring of degree zero operations. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Intermont-Strom/GoodSp Complexity and Good Spaces M. Intermont (Kalamazoo College) and J. Strom (Western Michigan University) intermon@kzoo.edu jeffrey.strom@wmich.edu This paper is an exploration of two ideas in the study of closed classes: the A-complexity of a space X and the notion of good spaces (spaces A for which C(A) = \overline{C(A)}). A variety of formulae for the computation of complexity are given, along with some calculations. Good spaces are characterized in terms of the functors CW_A and P_A. The main result is a countable upper bound for the complexity with respect to the suspension of A when A is a good space. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Jardine/stack-coh6 Title: Fibred sites and stack cohomology Author: J.F. Jardine AMS Classification numbers: 55P42, 18F20, 14A20 J.F. Jardine Department of Mathematics University of Western Ontario London, ON N6A 5B7 Canada E-mail: jardine@uwo.ca The usual notion of a site fibred over a stack is expanded to a definition of a site C/A fibred over a presheaf of categories A. Presheaves of simplicial sets on the site fibred over a presheaf of categories A are contravariant enriched diagrams defined on A, taking values in simplicial sets. The standard model structure for presheaves of simplicial sets induces a coarse equivariant structure for enriched contravariant A-diagrams. If the presheaf of categories is a presheaf of groupoids G, then the associated homotopy theory is Quillen equivalent to the homotopy theory of simplicial presheaves over BG, and so the homotopy theory for the fibred site C/G is an invariant of the homotopy type of G. Similar homotopy invariance results obtain for presheaves of spectra and presheaves of symmetric spectra on C/G. In particular, stack cohomology can be calculated on the fibred site for a representing presheaf of groupoids. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/Rezk/rezk-units-and-logs Title: The units of a ring spectrum and a logarithmic cohomology operation Author: Charles Rezk Authors e-mail address: rezk@math.uiuc.edu Abstract: We construct a ``logarithmic'' cohomology operation on Morava E-theory, which is a homomorphism defined on the multiplicative group of invertible elements in the ring E^0(K) of a space K. We obtain a formula for this map in terms of the action of Hecke operators on Morava E-theory. Our formula is closely related to that for an Euler factor of the Hecke L-function of an automorphic form. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/cohom Cohomology of $\lambda$-rings Donald Yau (University of Illinois at Urbana-Champaign), dyau@math.uiuc.edu A cohomology theory for $\lambda$-rings is developed. This is then applied to study deformations of $\lambda$-rings. 9. http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/lambda-rev2 On $\lambda$-ring structures over Z[[x]] Donald Yau (University of Illinois at Urbana-Champaign), dyau@math.uiuc.edu It is shown that the $\lambda$-ring structure over the power series ring Z[[x]] given by the $K$-theory of $CP^\infty$ is uniquely determined by the following condition: \psi^p(x) = px mod{x^2} for each prime $p$, where $\psi^p$ is the Adams operation. Applications to algebraic topology and formal group laws are given. 10. http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/truncated Extensions of filtered $\lambda$-ring structures over the dual number ring Donald Yau (University of Illinois at Urbana-Champaign), dyau@math.uiuc.edu We study problems related to the existence and uniqueness of filtered $\lambda$-ring structures over the truncated polynomial ring Z[x]/(x^3) that extend a given filtered $\lambda$-ring structure over Z[x]/(x^2). ---------------------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://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). 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.