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Witt vectors and equivariant ring spectra applied to cobordism
Author(s) -
Brun M.
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdl010
Subject(s) - subring , mathematics , cobordism , ring (chemistry) , pure mathematics , witt vector , noetherian ring , polynomial ring , functor , principal ideal ring , equivariant map , discrete mathematics , algebra over a field , polynomial , finitely generated abelian group , mathematical analysis , chemistry , organic chemistry
Given a finite group G we show that Dress and Siebeneicher's ring of G ‐typical Witt vectors on the Lazard ring, that is, on the polynomial ring on countably many indeterminates over the integers, embeds as a subring of the unitary cobordism ring of G ‐manifolds. We also show that the ring of G ‐typical Witt vectors on the Lazard ring embeds as a subring of the ring of homotopy groups of the G ‐fixed point spectrum of the spectrum MU representing cobordism. The above results are derived by exploiting the interaction between restriction, additive transfer and multiplicative transfer. This interaction is described by two Mackey functors satisfying a distributivity relation encoded in a formalism developed by Tambara.