For Complex Orientations Preserving Power Operations, p-typicality is Atypical

Details For Complex Orientations Preserving Power Operations, p-typicality is Atypical For Complex Orientations Preserving Power Operations, p-typicality is Atypical

2009-10-16

arxiv.org/abs/0910.3187v3

Topology and its Applications, Volume 157, Issue 14, 1 September 2010, Pages 2271-2288

Mathematics

Algebraic Topology

Minor revisions, results extended up to the prime 13. Accepted for publication. 22 pages

Scientific paper

10.1016/j.topol.2010.06.007

We show, for primes p less than or equal to 13, that a number of well-known MU_(p)-rings do not admit the structure of commutative MU_(p)-algebras. These spectra have complex orientations that factor through the Brown-Peterson spectrum and correspond to p-typical formal group laws. We provide computations showing that such a factorization is incompatible with the power operations on complex cobordism. This implies, for example, that if E is a Landweber exact MU_(p)-ring whose associated formal group law is p-typical of positive height, then the canonical map MU_(p) --> E is not a map of H_\infty ring spectra. It immediately follows that the standard p-typical orientations on BP, E(n), and E_n do not rigidify to maps of E_\infty ring spectra. We conjecture that similar results hold for all primes.

Affiliated with

Also associated with

No associations

Rating

For Complex Orientations Preserving Power Operations, p-typicality is Atypical 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 For Complex Orientations Preserving Power Operations, p-typicality is Atypical, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and For Complex Orientations Preserving Power Operations, p-typicality is Atypical will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-124419