Mathematics – Algebraic Topology
Scientific paper
2002-06-07
Mathematics
Algebraic Topology
17 pages. See also http://www.math.uchicago.edu/~may/99April1.pdf
Scientific paper
Hu, 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
Baker Andrew Jordan
May John P.
No associations
LandOfFree
Minimal Atomic Complexes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Minimal Atomic Complexes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimal Atomic Complexes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-522531