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Article overview
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The Whitehead group of the Novikov ring | | A.V.Pajitnov
; A.A.Ranicki
; | | Date: |
5 Dec 2000 | | Journal: | K-Theory 21 (2000) 325-365 | | Subject: | Algebraic Topology | math.AT | | Abstract: | The Bass-Heller-Swan-Farrell-Hsiang-Siebenmann decomposition of the Whitehead group $K_1(A_{
ho}[z,z^{-1}])$ of a twisted Laurent polynomial extension $A_{
ho}[z,z^{-1}]$ of a ring $A$ is generalized to a decomposition of the Whitehead group $K_1(A_{
ho}((z)))$ of a twisted Novikov ring of power series $A_{
ho}((z))=A_{
ho}[[z]][z^{-1}]$. The decomposition involves a summand $W_1(A,
ho)$ which is an abelian quotient of the multiplicative group $W(A,
ho)$ of Witt vectors $1+a_1z+a_2z^2+... in A_{
ho}[[z]]$. An example is constructed to show that in general the natural surjection $W(A,
ho)^{ab} o W_1(A,
ho)$ is not an isomorphism. | | Source: | arXiv, math.AT/0012031 | | Services: | Forum | Review | PDF | Favorites | |
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