The stable Adams conjecture and higher associative structures on Moore spectra [article]

Prasit Bhattacharya, Nitu Kitchloo
2021 arXiv   pre-print
In this paper, we provide a new proof of the stable Adams conjecture. Our proof constructs a canonical null-homotopy of the stable J-homomorphism composed with a virtual Adams operation, by applying the K-theory functor to a multi-natural transformation. We also point out that the original proof of the stable Adams conjecture is incorrect and present a correction. This correction is crucial to our main application. We settle the question on the height of higher associative structures on the mod
more » ... p^k Moore spectrum M_p(k) at odd primes. More precisely, for any odd prime p, we show that M_p(k) admits a Thomified 𝔸_n-structure if and only if n < p^k. We also prove a weaker result for p=2.
arXiv:1803.11014v3 fatcat:pb5b6zypvbeolebyqt4cy337yy