Abstract
Traditionally, localization is defined in the context of commutative algebra. However, ever since the work of Ore it has also been possible to localize noncommutative rings. High-dimensional knot theory requires the noncommutative localization matrix inversion method of Cohn [53], [54]. The algebraic K- and L-theory invariants of codimension 2 embeddings frequently involve this type of localization of a polynomial ring, as will become apparent in Part Two. (This is particularly the case for links, although links are beyond the scope of the book). The localization exact sequences of algebraic K- and L-theory also hold in the noncommutative case. This chapter deals with K-theory, and L-theory will be considered in Chap. 25.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ranicki, A. (1998). Noncommutative localization. In: High-dimensional Knot Theory. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12011-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-662-12011-8_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08329-7
Online ISBN: 978-3-662-12011-8
eBook Packages: Springer Book Archive