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Exotic multiplications on periodic complex bordism
Journal of Topology  (IF1.582),  Pub Date : 2020-11-04, DOI: 10.1112/topo.12169
Jeremy Hahn, Allen Yuan

Victor Snaith gave a construction of periodic complex bordism by inverting the Bott element in the suspension spectrum of $B U$. This presents an $E ∞$ structure on periodic complex bordism by different means than the usual Thom spectrum definition of the $E ∞$‐ring $M U P$. Here, we prove that these two $E ∞$‐rings are in fact different, though the underlying $E 2$‐rings are equivalent. Nonetheless, we prove that both rings $E ∞$‐orient $K U 2 ∧$ and other forms of $K$‐theory.