Blanchfield and Seifert algebra in high dimensional knot theory

Details Blanchfield and Seifert algebra in high dimensional knot theory Blanchfield and Seifert algebra in high dimensional knot theory

2002-12-13

arxiv.org/abs/math/0212187v3

Moscow Mathematical Journal 3, 1333-1367 (2003)

Mathematics

Geometric Topology

30 pages, LATEX. v3: minor revision of v2 (which was itself a minor revision of v1)

Scientific paper

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.

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