Blanchfield and Seifert algebra in high-dimensional knot theory. (English) Zbl 1059.19003

Ranicki, Andrew

Mosc. Math. J. 3, No. 4, 1333-1367 (2003).

Author’s abstract: The Blanchfield and Seifert forms of knot theory have algebraic analogues over arbitrary rings with involution. The covering Blanchfield form of a Seifert form is an algebraic analogue of the expression of the infinite cyclic cover of a knot complement as the infinite union of copies of a cobordism between two copies of a Seifert surface. The inverse construction of the Seifert form of a Blanchfield form is an algebraic analogue of the transversality construction of the Seifert surfaces of a knot as codimension 1 submanifolds of the knot complement.

Reviewer: Michael Farber (Zürich)

MSC:

19J25	Surgery obstructions (\(K\)-theoretic aspects)
57Q45	Knots and links in high dimensions (PL-topology) (MSC2010)

Keywords:

Blanchfield form; Seifert form; algebraic transversality