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

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Maths_RanickiA_Blanchfield and Seifert algebra Arxive.pdf (769.5Kb)
Date
01/11/2006
Author
Ranicki, Andrew
Sheiham, D.
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Abstract
The classification of high-dimensional μ–component boundary links motivates decomposition theorems for the algebraic K–groups of the group ring A[Fμ] and the noncommutative Cohn localization Σ-1A[Fμ], for any μ≥1 and an arbitrary ring A, with Fμ the free group on μ generators and Σ the set of matrices over A[Fμ] which become invertible over A under the augmentation A[Fμ]→A. Blanchfield A[Fμ]–modules and Seifert A–modules are abstract algebraic analogues of the exteriors and Seifert surfaces of boundary links. Algebraic transversality for A[Fμ]–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[Fμ]) and K*(Σ-1A[Fμ]) subject to a stable flatness condition on Σ-1A[Fμ] for the higher K–groups.
URI
http://www.msp.warwick.ac.uk/gt/2006/10/p043.xhtml

http://arxiv.org/PS_cache/math/pdf/0508/0508405v2.pdf

http://dx.doi.org/10.2140/gt.2006.10.1761

http://hdl.handle.net/1842/3005
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