6 papers this by time, by Ando, Bakuradze-Priddy, Bousfield, Kuhn, Martino-Priddy, and Zhou. Note that the paper by Zhou claims to prove that V(n) exists for all n and all p >= 5, contradicting Ravenel's proof that V(3) does not exist at p=5. Zhou claims that the Toda relation alpha_1 beta_1^p =0 is false, giving some reasons why Toda's proofs are wrong, and therefore Ravenel's argument does not apply. I am hoping one of you will clear this up, but in the meantime I should remind you that papers on the Hopf archive are not edited for correctness or anything else. Mark Hovey New papers appearing on hopf between 01/02/02 and 02/11/02 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Ando/ando-aeso Title: The sigma orientation for analytic circle-equivariant elliptic cohomology Author: Matthew Ando MSC: 55N34 (Primary); 55N22, 57R91 (Secondary) Arxiv: math.AT/0201092 Address: Department of Mathematics University of Illinois at Urbana-Champaign E-mail: mando@math.uiuc.edu Abstract: Let T be the circle group. We construct a canonical Thom isomorphism in T-equivariant analytic elliptic cohomology, for T-oriented virtual vector bundles bundles whose Borel-equivariant second Stiefel-Whitney and second Chern classes vanish. The construction is natural under pull-back of vector bundles and exponential under Whitney sum. It extends in the rational case the non-equivariant sigma orientation of Hopkins, Strickland, and the author. The construction relates the sigma orientation to the representation theory of loop groups and Looijenga's weighted projective space, and sheds light even on the non-equivariant case. Rigidity theorems of Witten-Bott-Taubes including generalizations by Kefeng Liu follow. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Bakuradze-Priddy/bp3b TRANSFER AND COMPLEX ORIENTED COHOMOLOGY RINGS MALKHAZ BAKURADZE AND STEWART PRIDDY Keywords: transfer, Chern class, classifying space, complex cobor- dism, Morava K-theory 55N22, 55R12. 1. Introduction Let p be a prime and let G be a subgroup of the symmetric group S_p. In this paper we use the transfer to study homotopy orbit spaces X^p_hG= EG x_G X^p in complex oriented cohomology. We are particularly interested in computing the ring structure. Thus we are led to consider the relation between cup products and transfer known as Fröbenius reciprocity by analogy with representation theory Tr*(x)y = Tr*(x rho*(y)) (formula (i) of Section 2) where rho : EG x X^p --> X^p_hG is the covering projection and Tr* : E*(X^p) ---> E*(X^p_hG) is the associated transfer homomorphism. It is worth noting that the multiplicative structure of the cohomology groups we consider is com- pletely determined by this formula. In case E = K(s) is Morava K-theory, G is cyclic of order p, and X is the classifying space of a finite group, Hopkins-Kuhn-Ravenel [11 ] have studied these cohomology groups as modules over the coefficient ring. Our paper builds on their approach by extending their notion of a good group to spaces. For X = CP^infty we determine the algebra K(s)*(X^p_hS_p) for Morava K-theory; for complex cobordism we compute the ring MU*(X^p_hS_p) making additional use of the formal group law. This enables us to make explicit computations of the transfer in both cases. In an analogous fashion we compute the algebra BP *(X^p_hS_p). The starting point and original motivation for our work comes from Quillen's famous formula for Tr*(1), the stable Euler class, for the uni- versal Z/p covering. As explained in Section 2, our results for CP^infty provide a universal example which enable us to compute the stable Eu- ler classes and the transfer in general for many other cases. For example universal coverings for some nonabelian p-groups, namely those with cyclic subgroups of index p and those which are semi-direct products of elementary abelian p-groups with Z/p. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Bousfield/cosim Cosimplicial resolutions and homotopy spectral sequences in model categories A.K. Bousfield Mathematics Subject Classification. Primary 55U35; Secondary 18G55, 55P60, 55T15. Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago Chicago, IL 60607 bous@uic.edu We develop a general theory of cosimplicial resolutions, homotopy spectral sequences, and completions for objects in model categories, extending work of Bousfield-Kan and Bendersky-Thompson for ordinary spaces. This is based on a generalized cosimplicial version of the Dwyer-Kan-Stover theory of resolution model categories, and we are able to construct our homotopy spectral sequences and completions using very flexible weak resolutions in the spirit of relative homological algebra. We deduce that our completion functors have triple structures and preserve certain fiber squares up to homotopy. We also deduce that the Bendersky-Thompson completions over connective ring spectra are equivalent to Bousfield-Kan completions over solid rings. The present work allows us to show, in a subsequent paper, that the Bendersky-Thompson homotopy spectral sequences over arbitrary ring spectra have well-behaved composition pairings. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/Kuhn/kuhn-mc Title: The McCord model for the tensor product of a space and a commutative ring spectrum. Author: Nicholas J. Kuhn AMS classification: Primary 55P43; Secondary 18G55 Author's address: Department of Mathematics, University of Virginia, Charlottesville, VA 22904 Email: njk4x@virginia.edu Abstract: This paper begins by noting that, in a 1969 paper in the Transactions, M.C.McCord introduced a construction that can be interpreted as a model for the categorical tensor product of a based space and a topological abelian group. This can be adapted to Segal's very special Gamma--spaces, and then to a more modern situation: (K tensor R) where K is a based space and R is a unital, augmented, commutative, associative S--algebra. The model comes with an easy-to-describe filtration. If one lets K = S^n, and then stabilize with respect to n, one gets a filtered model for the Topological Andre--Quillen Homology of R. When R = Omega^{infty} Sigma^{infty} X, one arrives at a filtered model for the connective cover of a spectrum X, constructed from its 0th space. Another example comes by letting K be a finite complex, and R the S--dual of a finite complex Z. Dualizing again, one arrives at G.Arone's model for the Goodwillie tower of the functor sending Z to the suspension spectrum of Map(K,Z). Applying cohomology with field coefficients, one gets various spectral sequences for deloopings with known E_1--terms. A few nontrivial examples are given. In an appendix, we describe the construction for unital, commutative, associative S--algebras not necessarily augmented. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/Martino-Priddy/mobiushopf Minami-Webb type decompositions for compact Lie groups John Martino and Stewart Priddy We extend to compact Lie groups some stable classifying space decompositions of Minami, following Webb. One notable feature of Webb's work is the use of a combinatorial Möbius function to encode p-local information about the cohomology of a finite group. We wish to show similar phenomena hold for compact Lie groups. However, for a compact Lie group G one is faced with the problem of an infinite number of conjugacy classes of p-toral subgroups, that is, extensions of tori by finite p-groups. These groups are the analogs of p-groups for finite groups. We circumvent this problem by considering a certain finite G-complex which allows us to introduce combinatorial methods in the compact Lie group case. This complex is based on the notion of p-stubborn subgroups which arose earlier in modular representation theory of finite groups (where they were called p-radical groups) in connection with Alperin's conjecture in group cohomology and in the study of homotopy classes of maps between classifying spaces of compact Lie groups. We also derive a decomposition based on the corresponding complex for elementary abelian p-subgroups. Several examples are given to illustrate the various decompositions. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/ZhouXueguang/zzhou (See the disclaimer at the top of this announcement). Smith-Toda Spectrum $V(\infty)$ exists for all $p\geqslant 5$} Zhou Xueguang AMS classification numbers: 55Q Address of author: Department of Mathematics, Nankai University, Tianjin 300071, People's Republic of China Email address of author: zhengqb@eyou.co Abstract In this paper, we prove that the Smith-Toda spectrum $V(n)$ exists for all non-negative integers $n$.