The Whitehead group of the Novikov ring
Pajitnov, A. V. · Ranicki, A. A.
Original · EN
The Bass-Heller-Swan-Farrell-Hsiang-Siebenmann decomposition of the Whitehead group K₁(Aρ[z,z⁻¹]) of a twisted Laurent polynomial extension Aρ[z,z⁻¹] of a ring A is generalized to a decomposition of the Whitehead group K₁(Aρ((z))) of a twisted Novikov ring of power series Aρ((z))=Aρ[[z]][z⁻¹]. The decomposition involves a summand W₁(A,ρ) which is an abelian quotient of the multiplicative group W(A,ρ) of Witt vectors 1+a₁z+a₂z²+... ∈ Aρ[[z]]. An example is constructed to show that in general the natural surjection W(A,ρ)ab → W₁(A,ρ) is not an isomorphism.
English translation
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