Location of Repository

MINIMAL ATOMIC COMPLEXES

By 

Abstract

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, eo2, and BoP at the prime 2, all BP 〈n 〉 at any prime p, and the indecomposable wedge summands of Σ∞CP ∞ and Σ∞HP ∞ at any prime p are minimal atomic

Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.170.3904
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • http://www.math.uiuc.edu/K-the... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.