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- W2963804949 abstract "For a multiplicative cohomology theory E, complex orientations are in bijective correspondence with multiplicative natural transformations to E from complex bordism cohomology MU. If E is represented by a spectrum with a highly structured multiplication, we give an iterative process for lifting an orientation $$MU rightarrow E$$ to a map respecting this extra structure, based on work of Arone–Lesh. The space of strictly commutative orientations is the limit of an inverse tower of spaces parametrizing partial lifts; stage 1 corresponds to ordinary complex orientations, and lifting from stage $$(m-1)$$ to stage m is governed by the existence of an orientation for a family of E-modules over a fixed base space $$F_m$$ . When E is p-local, we can say more. We find that this tower only changes when m is a power of p, and if E is E(n)-local the tower is constant after stage $$p^n$$ . Moreover, if the coefficient ring $$E^*$$ is p-torsion free, the ability to lift from stage 1 to stage p is equivalent to a condition on the associated formal group law that was shown necessary by Ando." @default.
- W2963804949 created "2019-07-30" @default.
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- W2963804949 date "2017-12-18" @default.
- W2963804949 modified "2023-09-28" @default.
- W2963804949 title "Strictly commutative complex orientation theory" @default.
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- W2963804949 doi "https://doi.org/10.1007/s00209-017-2009-6" @default.
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