Minimal Atomic Complexes

dc.creatorBaker, A. J.
dc.creatorMay, J. P.
dc.date2002-06-07
dc.date.accessioned2026-07-07T04:48:57Z
dc.date.available2026-07-07T04:48:57Z
dc.descriptionHu, Kriz and May recently reexamined ideas implicit in Priddy's elegant homotopy theoretic construction of the Brown-Peterson spectrum at a prime p. They discussed May's notions of nuclear complexes and of cores of spaces, spectra, and commutative S-algebras. Their most striking conclusions, due to Hu and Kriz, were negative: cores are not unique up to equivalence, and BP is not a core of MU considered as a commutative S-algebra, although it is a core of MU considered as a p-local spectrum. We investigate these ideas further, obtaining much more positive conclusions. We show that nuclear complexes have several non-obviously equivalent characterizations. Up to equivalence, they are precisely the irreducible complexes, the minimal atomic complexes, and the Hurewicz complexes with trivial mod p Hurewicz homomorphism above the Hurewicz dimension, which we call complexes with no mod p detectable homotopy. Unlike the notion of a nuclear complex, these other notions are all invariant under equivalence. This simple and conceptual criterion for a complex to be minimal atomic allows us to prove that many familiar spectra, such as ko, eo_2, and BoP at the prime 2, all BP<n> at any prime p, and the indecomposable wedge summands of the suspension spectra of $CP^\infty$ and $HP^\infty$ at any prime p are minimal atomic.
dc.description17 pages. See also http://www.math.uchicago.edu/~may/99April1.pdf
dc.identifierhttps://arxiv.org/abs/math/0206067
dc.identifierhttp://arxiv.org/abs/math/0206067
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64245
dc.subjectAlgebraic Topology
dc.subject55P15, 55P42, 55P60
dc.titleMinimal Atomic Complexes
dc.typetext

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