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• W2328892419 abstract "0. Introduction. This paper examines the homotopy type of the Thom spectrum MSU associated with special unitary cobordism. For odd primes p, standard methods show that the p-localization MSU(p) is equivalent to a wedge of suspensions of the Brown-Peterson spectrum BP. Forp = 2, however, this is not the case, and our work is devoted to determining the 2-primary homotopy type of MSU. This involves a new indecomposable spectrum, and our main results are the following. There is an indecomposable 2-local spectrum, which we call BoP, such that MSU(2) is equivalent to a wedge of suspensions of BoP and BP. Under the equivalence, the Thom class lies in a BoP summand. As a comodule over the dual Steenrod algebra A [11], H*(BoP; Z/2) is a sum of 4 '2 2 suspensions of B = Z/2[?1, t2, ..., j, . ... C A, where tj is the conjugate of Milnor's generator (j. There is one suspension of B beginning in each nonnegative dimension divisible by 8. BoP bears strong similarities to BP and the (1)-connected K-theory spectra bo and bu. In particular, in Section 6 we show there is a map BoP bo(2) inducing an epimorphism v* of homotopy groups. In fact, v* induces an isomorphism of torsion subgroups, and its torsion free kernel is concentrated in even dimensions. A brief summary of our methods is as follows. In Sections 1 and 2 we describe the Adams spectral sequence for 7r*MSU(2), including a computation of the differentials, with particular attention paid to the product structure. Anderson, Brown, and Peterson [4] gave a computation for these differentials, but their proof requires some correction, and in any case we will need the more extensive knowledge of the product structure. In Sections 3 to 5, we construct BoP and show it is indecomposable. To produce BoP, first the Sullivan-Baas construction is applied to MSU, yielding a spectrum representing a bordism theory of SU-manifolds with" @default.
• W2328892419 created "2016-06-24" @default.
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• W2328892419 date "1982-10-01" @default.
• W2328892419 modified "2023-10-18" @default.
• W2328892419 title "The Homotopy Type of MSU" @default.
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• W2328892419 doi "https://doi.org/10.2307/2374085" @default.
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