Secondary power operations and the Brown--Peterson spectrum at the prime 2
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چکیده
منابع مشابه
Secondary power operations and the Brown–Peterson spectrum at the prime 2
The dual Steenrod algebra has a canonical subalgebra isomorphic to the homology of the Brown–Peterson spectrum. We will construct a secondary operation in mod-2 homology and show that this canonical subalgebra is not closed under it. This allows us to conclude that the 2-primary Brown–Peterson spectrum does not admit the structure of an En -algebra for any n ≥ 12, answering a question of May in...
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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 estima...
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An algebraic criterion, in terms of closure under power operations, is determined for the existence and uniqueness of generalized truncated Brown-Peterson spectra of height 2 as E∞-ring spectra. The criterion is checked for an example at the prime 2 derived from the universal elliptic curve equipped with a level Γ1(3) structure. 2000MSC: 55P42, 55P43, 55N22 and 14L05
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2018
ISSN: 0003-486X
DOI: 10.4007/annals.2018.188.2.3