Exotic multiplications on periodic complex bordism

摘要

Victor Snaith gave a construction of periodic complex bordism by inverting the Bott element in the suspension spectrum of BU. This presents an E infinity structure on periodic complex bordism by different means than the usual Thom spectrum definition of the E infinity-ring MUP. Here, we prove that these two E infinity-rings are in fact different, though the underlying E2-rings are equivalent. Nonetheless, we prove that both rings E infinity-orient KU2 perpendicular to and other forms of K-theory.