Celebratio Mathematica — Ranicki

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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

G. Segal, H. Bass, M. Atiyah, K. Brown, J. Cuntz, J. Duflot, J.-L. Loday, A. Ranicki, B. Mazur, D. Sullivan, U. Tillmann, and J. Quillen: “Daniel Quillen,” Notices Am. Math. Soc. 59 : 10 (2012), pp. 1392–1406. Eric Friedlander and Daniel Grayson were coordinating editors. MR 3025899 Zbl 1284.01060 article

M. F. Atiyah	Related	Volume
Eric Mark Friedlander	Related
Dennis P. Sullivan	Related
Jean-Louis Loday	Related
Daniel Gray Quillen	Related
Ulrike Tillmann	Related
Barry C. Mazur	Related
Graeme Bryce Segal	Related
Joachim J. R. Cuntz	Related
Hyman Bass	Related
Daniel Richard Grayson	Related
Jeanne Duflot	Related
Kenneth Stephen Brown	Related