Abstract
Automorphism K-theory is the algebraic K-theory of modules with an automorphism, such as arise from fibred knots. An A-module M with an automorphism h : M → M is essentially the same as a module M over the Laurent polynomial ring A[z, z −1], with the invertible indeterminate z acting on M by h. This correspondence will be used to express the various automorphism K-groups of A in terms of the algebraic K-groups K * (Σ −1 A[z, z −1]) of the localizations Σ −1 A[z, z −1] inverting appropriate sets Σ of square matrices in A[z, z −1].
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© 1998 Springer-Verlag Berlin Heidelberg
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Ranicki, A. (1998). Automorphism K-theory. In: High-dimensional Knot Theory. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12011-8_13
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DOI: https://doi.org/10.1007/978-3-662-12011-8_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08329-7
Online ISBN: 978-3-662-12011-8
eBook Packages: Springer Book Archive