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arXiv:math/0212187 [math.GT]AbstractReferencesReviewsResources

Blanchfield and Seifert algebra in high dimensional knot theory

Andrew Ranicki

Published 2002-12-13, updated 2003-01-13Version 3

Novikov initiated the study of the algebraic properties of quadratic forms over polynomial extensions by a far-reaching analogue of the Pontrjagin-Thom transversality construction of a Seifert surface of a knot and the infinite cyclic cover of the knot exterior. In this paper the analogy is applied to explain the relationship between the Seifert forms over a ring with involution and Blanchfield forms over the Laurent polynomial extension.

Comments: 30 pages, LATEX. v3: minor revision of v2 (which was itself a minor revision of v1)
Journal: Moscow Mathematical Journal 3, 1333-1367 (2003)
Categories: math.GT, math.AT
Subjects: 57R67
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