Abstract. We improve on some results with Ravenel and Yagita in a paper by the same name. In particular, we generalize when injectivity, surjectivity, and exactness of Morava K-theory implies the same for Brown-Peterson cohomology. A type of flatness is no longer assumed, but instead it is a consequence of weaker assumptions. The main application is an easier proof that QS 2k+1 has this flatness property. In addition, we show that if elements in the Brown-Peterson cohomology generate all of the Morava K-theories, then they also generate the Brown-Peterson cohomology and it is Landweber flat.
In this paper, we study applications of Atiyah–Hirzebruch spectral sequences for motivic cobordism recently found by Hopkins and Morel. For example, we compute the mod 2 motivic cohomology of a reduced Cech complex of a splitting variety according to Orlov, Vishik and Voevodsky. The cobordism ring MGL / 2*, * (Spec(R)) is computed and compared with the results of the real cobordism theory of Hu and Kriz. Moreover, we study algebraic cobordism of the classifying spaces BG for algebraic groups over C. For example, the Chow ring CH∗false(BG2false)(2false) for the exceptional Lie group G2 is determined by using motivic cobordism and motivic cohomology. 2000 Mathematics Subject Classification 55P36, 57T25 (primary), 55R36, 57T05 (secondary).
Abstract. The Steenrod algebra structures of H*{BG; Z/p) for compact Lie groups are studied. Using these, Brown-Peterson cohomology and Morava Ktheory are computed for many concrete cases. All these cases have properties similar as torsion free Lie groups or finite groups, e.g., BPodá{BG) = 0.
This article contains a collection of problems contributed during the course of the conference.
55PXX; 55SXX1 The problems presented by Carles Broto Broto, Levi and Oliver [1,2] introduced the concept of p-local finite group as an algebraic object modeled on the fusion on the Sylow p-subgroup of a finite group, and attached to it a classifying space which is a p-complete space with properties similar to that of the p-completed classifying space of a finite group. Every finite group G gives rise canonically to a p-local finite group with classifying space homotopy equivalent to BG ∧ p . But there are also exotic examples; that is, p-local finite groups that cannot be obtained from a finite group in the canonic way and therefore its classifying space is not homotopy equivalent to the p-completed classifying space of any finite group.Some exotic examples are obtained by Broto and Møller [3] out of p-compact groups (see and Møller [7]). More precisely, to a 1-connected pcompact group X it is attached a family X(q) of p-local finite groups, q a p-adic unit, that approximates X in the sense that the classifying spaces {BX(q p m )} m∈N form a direct system with mapping telescope hocolim m BX(q p m ) BX
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