A lower bound for coherences on the Brown–Peterson spectrum

Richter, Birgit

doi:10.2140/agt.2006.6.287

Richter, Birgit ¹

¹Fachbereich Mathematik der Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany

Algebraic and Geometric Topology, Tome 6 (2006) no. 1, pp. 287-308

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Résumé

We provide a lower bound for the coherence of the homotopy commutativity of the Brown–Peterson spectrum, BP, at a given prime p and prove that it is at least (2p2 + 2p − 2)–homotopy commutative. We give a proof based on Dyer–Lashof operations that BP cannot be a Thom spectrum associated to n–fold loop maps to BSF for n = 4 at 2 and n = 2p + 4 at odd primes. Other examples where we obtain estimates for coherence are the Johnson–Wilson spectra, localized away from the maximal ideal and unlocalized. We close with a negative result on Morava-K–theory.

DOI : 10.2140/agt.2006.6.287

Keywords: structured ring spectra, Brown-Peterson spectrum

Affiliations des auteurs :

Richter, Birgit ¹

¹ Fachbereich Mathematik der Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany

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Richter, Birgit. A lower bound for coherences on the Brown–Peterson spectrum. Algebraic and Geometric Topology, Tome 6 (2006) no. 1, pp. 287-308. doi: 10.2140/agt.2006.6.287

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