This second part contains 8 new papers, 2 from Moller, 1 from Oliver, and 5, count 'em 5, from YauD. Mark Hovey New papers appearing on hopf between 09/11/02 and 10/07/02, part 2 1. http://hopf.math.purdue.edu/cgi-bin/generate?/Moller/ndet Title of paper: N-determined p-compact groups Author: Jesper M. Moller AMS Classification numbers: 55R35, 55P15 Email address of Author: moller@math.ku.dk Abstract: We consider p-compact groups where p is an odd primes. The paper contains a classification of p-compact groups, excluding the E-family, in terms of maximal torus normalizers. 2. http://hopf.math.purdue.edu/cgi-bin/generate?/Moller/twocgs Author: Jesper Moller Title: The 2-compact groups in the A-family are N-determined Let G be compact Lie group locally isomorphic to SU(n) for some n. The 2-completion of the classifyong space BG is a 2-compact group in the A-family. We show that these 2-compact groups are determined up to isomorphism by their maximal torus normalizers. 3. http://hopf.math.purdue.edu/cgi-bin/generate?/Oliver/limz-odd Author: Bob Oliver Title: Equivalences of classifying spaces completed at odd primes We prove here the Martino-Priddy conjecture for an odd prime p: the p-completions of the classifying spaces of two groups G and G' are homotopy equivalent if and only if there is an isomorphism between their Sylow p-subgroups which preserves fusion. A second theorem is a description for odd p of the group of homotopy classes of self homotopy equivalences of the p-completion of BG, in terms of automorphisms of a Sylow p-subgroup of G which preserve fusion in G. These are both consequences of a technical algebraic result, which says that for an odd prime p and a finite group G, all higher derived functors of the inverse limit vanish for a certain functor on the p-subgroup orbit category of G. 4. http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/adic_genus2 Title: On adic genus, Postnikov conjugates, and lambda-rings Author: Donald Yau MSC: 55P15; 55N15, 55P60, 55S25 Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801 dyau@math.uiuc.edu Sufficient conditions on a space are given which guarantee that the $K$-theory ring and the ordinary cohomology ring with coefficients over a principal ideal domain are invariants of, respectively, the adic genus and the SNT set. An independent proof of Notbohm's theorem on the classification of the adic genus of $BS^3$ by $KO$-theory $\lambda$-rings is given. An immediate consequence of these results about adic genus is that for any positive integer $n$, the power series ring $\bZ \lbrack \lbrack x_1, \ldots , x_n \rbrack \rbrack$ admits uncountably many pairwise non-isomorphic $\lambda$-ring structures. 5. http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/moduli2 Title: Moduli space of filtered lambda-ring structures over a filtered ring Author: Donald Yau MSC: 16W70, 13K05, 13F25 Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801 dyau@math.uiuc.edu Motivated by recent works on the genus of classifying spaces of compact Lie groups, here we study the set of filtered $\lambda$-ring structures over a filtered ring from a purely algebraic point of view. From a global perspective, we first show that this set has a canonical topology compatible with the filtration on the given filtered ring. For power series rings $R \llbrack x \rrbrack$, where $R$ is between $\bZ$ and $\bQ$, with the $x$-adic filtration, we mimic the construction of the Lazard ring in formal group theory and show that the set of filtered $\lambda$-ring structures over $R \llbrack x \rrbrack$ is canonically isomorphic to the set of ring maps from some ``universal'' ring $U$ to $R$. From a local perspective, we demonstrate the existence of uncountably many mutually non-isomorphic filtered $\lambda$-ring structures over some filtered rings, including rings of dual numbers over binomial domains, (truncated) polynomial and powers series rings over torsionfree $\bQ$-algebras. 6. http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/nonexistence_final_2 Title: Maps to spaces in the genus of infinite quaternionic projective space Author: Donald Yau MSC: 55S37, 55S25 Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801 dyau@math.uiuc.edu Spaces in the genus of infinite quaternionic projective space which admit essential maps from infinite complex projective space are classified. In these cases the sets of homotopy classes of maps are described explicitly. These results strengthen the classical theorem of McGibbon and Rector on maximal torus admissibility for spaces in the genus of infinite quaternionic projective space. An interpretation of these results in the context of Adams-Wilkerson embedding in integral $K$-theory is also given. 7. http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/steenrod_kuhn Title: Algebra over the Steenrod algebra, lambda-ring, and Kuhn's Realization Conjecture Author: Donald Yau Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801 dyau@math.uiuc.edu In this paper we study the relationships between operations in $K$-theory and ordinary mod $p$ cohomology. In particular, conditions are given under which the mod $p$ associated graded ring of a filtered $\lambda$-ring is an unstable algebra over the Steenrod algebra. This result partially extends to the algebraic setting a topological result of Atiyah about operations on $K$-theory and mod $p$ cohomology for torsionfree spaces. It is also shown that any polynomial algebra that is an algebra over the Steenrod algebra can be realized as the mod $p$ associated graded of a filtered $\lambda$-ring. Another observation is that Atiyah's result gives rise to a $K$-theoretic analogue of Kuhn's Realization Conjecture concerning the size of spaces in cohomology. 8. http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/unstable Title: Unstable $K$-cohomology algebra is filtered lambda-ring Author: Donald Yau MSC: 55N20,55N15,55S05,55S25 Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, IL 61801 dyau@math.uiuc.edu Boardman, Johnson, and Wilson gave a precise formulation for an unstable algebra over a generalized cohomology theory. Modifying their definition slightly in the case of complex $K$-theory by taking into account its periodicity, we prove that an unstable algebra for complex $K$-theory is precisely a filtered $\lambda$-ring, and vice versa. ---------------