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Proceedings of the London Mathematical Society Advance Access originally published online on November 27, 2006
Proceedings of the London Mathematical Society 2007 94(2):351-385; doi:10.1112/plms/pdl010
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© 2006 London Mathematical Society

Witt vectors and equivariant ring spectra applied to cobordism

M. Brun

Department of Mathematics
University of Bergen
Johannes Brunsgate 12
N-5008 Bergen
Norway
morten.brun{at}uib.no

Received 25 November 2004. Revision received 8 March 2006.

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.


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