Subject: new Hopf listings From: Mark Hovey Date: 06 Oct 2006 09:12:13 -0400 I took a month off; sorry about the delay. There are 9 new papers this time, from Bergner, Chebolu-Christensen-Minac, DavisDaniel, Dugger-Isaksen, Fausk (2), GrayB, Hovey-Lockridge-Puninski, and Wuethrich. Mark Hovey New papers appearing on hopf between 8/4/06 and 10/6/06 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Bergner/ReedyFib Title: A characterization of fibrant Segal categories Author: Julia E. Bergner AMS Classification: 55U35, 18G30 Author's address: Kansas State University 138 Cardwell Hall Manhattan, KS 66506 Abstract: In this note we prove that Reedy fibrant Segal categories are fibrant objects in the model category structure Secat_c. Combining this result with a previous one, we thus have that the fibrant objects are precisely the Reedy fibrant Segal categories. We also show that the analogous result holds for Segal categories which are fibrant in the projective model structure on simplicial spaces, considered as objects in the model structure Secat_f. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Chebolu-Christensen-Minac/ghost [Note: I had trouble with the dvi file of this paper. I expect to have it up by 10/7/06--Mark] TITLE: Ghosts in modular representation theory AUTHORS: Sunil K. Chebolu, J. Daniel Christensen, and Jan Minac Department of Mathematics University of Western Ontario London, ON N6A 5B7, Canada AMS Subject classsification: Primary 20C20, 20J06; Secondary 55P42 ABSTRACT: We study ghosts in the stable module category of a finite group. That is, we study maps between modular representations of finite groups which are invisible in Tate cohomology. We establish various sets of conditions which guarantee the existence of a non-trivial ghost out of a given representation. We then investigate the generating hypothesis which is the statement that there are no non-trivial ghosts between finite-dimensional representations. This is done by focusing on three quintessential examples: the cyclic $p$-groups (finite representation type), the Klein four group (domestic representation type), and the quaternion groups (tame representation type). In the examples where the generating hypothesis fails, we obtain bounds on the ghost number: the smallest integer $l$ such that the composition of any $l$ ghosts between finite-dimensional representations is trivial. In particular, we obtain bounds on the ghost numbers for all $2$-groups which have a cyclic subgroup of index $2$. Projective classes in the stable module category play a key role in getting these bounds. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/DavisDaniel/subhg3 Title: The homotopy orbit spectrum for profinite groups Author: Daniel G. Davis Abstract: Let G be a profinite group. We define an S[[G]]-module to be a G-spectrum X that satisfies certain conditions, and, given an S[[G]]-module X, we define the homotopy orbit spectrum X_{hG}. When G is countably based and X satisfies a certain finiteness condition, we construct a homotopy orbit spectral sequence whose E_2-term is the continuous homology of G with coefficients in the graded profinite Z[[G]]-module pi_*X. Let G_n be the extended Morava stabilizer group and let E_n be the Lubin-Tate spectrum. As an application of our theory, we show that the function spectrum F(E_n,L_{K(n)}(S0)) is an S[[G_n]]-module with an associated homotopy orbit spectral sequence. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Dugger-Isaksen/etdq Title: Etale homotopy and sums-of-squares formulas Authors: Daniel Dugger, Daniel C. Isaksen AMS classification number: 55P60, 15A63 Abstract: This paper uses a relative of BP-cohomology to prove a theorem in characteristic p algebra. Specifically, we obtain some new necessary conditions for the existence of sums-of-squares formulas over fields of characteristic p > 2. These conditions were previously known in characteristic zero by results of Davis. Our proof uses a generalized etale cohomology theory called etale BP2. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Fausk/ArtinBrauer Generalized Artin and Brauer induction for compact Lie groups Halvard Fausk Abstract: Let $G$ be a compact Lie group. We present two induction theorems for certain generalized $G$-equivariant cohomology theories. The theory applies to $G$-equivariant $K$-theory $K_G$, and to the Borel cohomology associated to any complex oriented cohomology theory. The coefficient ring of $K_G$ is the representation ring $R(G)$ of $G$. When $G$ is a finite group the induction theorems for $K_G$ coincide with the classical Artin and Brauer induction theorems for $R(G)$. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/Fausk/Gspectra-Fausk Title: Equivariant homotopy theory for pro--spectra Author: Halvard Fausk Abstract. We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The $G-$homotopy theory is ``pieced together'' from the $G/U-$homotopy theories for suitable quotient groups $G/U$ of $G$; a motivation is the way continuous group cohomology of a profinite group is built out of the cohomology of its finite quotient groups. In this category Postnikov towers are studied from a general perspective. We introduce pro$-G-$spectra and construct various model structures on them. A key property of the model structures is that pro-spectra are weakly equivalent to their Postnikov towers. We give a careful discussion of two version of a model structure with ``underlying weak equivalences''. One of the versions only make sense for pro$-$spectra. In the end we use the theory to study homotopy fixed points of pro$-G-$spectra. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/GrayB/fiber Filtering the fiber of the pinch map Brayton Gray This paper develops the similarity between the loops on an odd dimensional sphere and the fiber F of the pinch map from an odd dimensional mod p^r Moore space to the sphere, for p odd. In particular, a Hopf invariant map is defined and there is an EHP sequence up to a factor which is the loops on a bouquet of higher dimensiona Moore spaces. As a consequence we have two technical results about the mysterious connecting map from the double loops on the sphere to the loops on F. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/Hovey-Lockridge-Puninski/derived-gen-hyp Title: The generating hypothesis in the derived category of a ring. Authors: Mark Hovey, Keir Lockridge, and Gena Puninski Abstract: We show that a strong form (the fully faithful version) of the generating hypothesis, introduced by Freyd in algebraic topology, holds in the derived category of a ring R if and only if R is von Neumann regular. This extends results of the second author. We also characterize rings for which the original form (the faithful version) of the generating hypothesis holds in the derived category of R. These must be close to von Neumann regular in a precise sense, and, given any of a number of finiteness hypotheses, must be von Neumann regular. However, we construct an example of such a ring that is not von Neumann regular, and therefore does not satisfy the strong form of the generating hypothesis. 9. http://hopf.math.purdue.edu/cgi-bin/generate?/Wuethrich/thickenings_rev Title: Infinitesimal thickenings of Morava K-theories (revised version) Author: Samuel Wuethrich AMS classification number: 55P42, 55P43; 55U20, 55N22 Abstract: This is a revised version. A few points have been clarified and some typos have been corrected. A. Baker has constructed certain sequences of cohomology theories which interpolate between the Johnson-Wilson and the Morava K-theories. We realize the representing sequences of spectra as sequences of MU-algebras. Starting with the fact that the spectra representing the Johnson-Wilson and the Morava K-theories admit such structures, we construct the sequences by inductively forming singular extensions. Our methods apply to other pairs of MU-algebras as well. ---------------------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.