Celebratio Mathematica — Ranicki

Complete Bibliography

Works connected to Andrei Vladimirovich Pajitnov

Filter the Bibliography List

year	title	people

			clear

A. V. Pajitnov and A. A. Ranicki: “The Whitehead group of the Novikov ring,” \( K \)-Theory 21 : 4 (2000), pp. 325–365. MR 1828181 Zbl 0996.19002 ArXiv math/0012031 article

The Bass–Heller–Swan–Farrell–Hsiang–Siebenmann decomposition of the Whitehead group \[ K_1(A_{\rho}[z,z^{-1}]) \] of a twisted Laurent polynomial extension \( A_{\rho}[z,z^{-1}] \) of a ring \( A \) is generalized to a decomposition of the Whitehead group \( K_1(A_{\rho}((z))) \) of a twisted Novikov ring of power series \[ A_{\rho}((z)) = A_{\rho}[[z]]\,[z^{-1}] .\] The decomposition involves a summand \( W_1(A,\rho) \) which is an Abelian quotient of the multiplicative group \( W(A,\rho) \) of Witt vectors \[ 1 + a_1z + a_2z^2 + \dots \in A_{\rho}[[z]] .\] An example is constructed to show that in general the natural surjection \[ W(A,\rho)^{ab}\to W_1(A,\rho) \] is not an isomorphism.

Daniel Gray Quillen	Related
Andrei Vladimirovich Pajitnov	Related