Blanchfield and Seifert algebra in high-dimensional boundary link theory I: Algebraic K-theory

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dc.creatorRanicki, Andrew
dc.creatorSheiham, Desmond
dc.date2005-08-22
dc.date2009-03-02
dc.date.accessioned2026-07-07T12:47:44Z
dc.date.available2026-07-07T12:47:44Z
dc.descriptionThe classification of high-dimensional mu-component boundary links motivates decomposition theorems for the algebraic K-groups of the group ring A[F_mu] and the noncommutative Cohn localization Sigma^{-1}A[F_mu], for any mu>0 and an arbitrary ring A, with F_mu the free group on mu generators and Sigma the set of matrices over A[F_mu] which become invertible over A under the augmentation A[F_mu] to A. Blanchfield A[F_mu]-modules and Seifert A-modules are abstract algebraic analogues of the exteriors and Seifert surfaces of boundary links. Algebraic transversality for A[F_mu]-module chain complexes is used to establish a long exact sequence relating the algebraic K-groups of the Blanchfield and Seifert modules, and to obtain the decompositions of K_*(A[F_mu]) and K_*(Sigma^{-1}A[F_mu]) subject to a stable flatness condition on Sigma^{-1}A[F_mu] for the higher K-groups.
dc.descriptionThis is the version published by Geometry & Topology on 2 November 2006
dc.identifierhttps://arxiv.org/abs/math/0508405
dc.identifierhttp://arxiv.org/abs/math/0508405
dc.identifierGeom. Topol. 10 (2006) 1761-1853
dc.identifierdoi:10.2140/gt.2006.10.1761
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221822
dc.subjectAlgebraic Topology
dc.subjectGeometric Topology
dc.subject19D50, 57Q45, 20E05
dc.titleBlanchfield and Seifert algebra in high-dimensional boundary link theory I: Algebraic K-theory
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