Invariants of Boundary Link Cobordism II. The Blanchfield-Duval Form
Abstract
Description
We use the Blanchfield-Duval form to define complete invariants for the cobordism group C_{2q-1}(F_μ) of (2q-1)-dimensional μ-component boundary links (for q\geq2).
The author solved the same problem in math.AT/0110249 via Seifert forms. Although Seifert forms are convenient in explicit computations, the Blanchfield-Duval form is more intrinsic and appears naturally in homology surgery theory.
The free cover of the complement of a link is constructed by pasting together infinitely many copies of the complement of a μ-component Seifert surface. We prove that the algebraic analogue of this construction, a functor denoted B, identifies the author's earlier invariants with those defined here. We show that B is equivalent to a universal localization of categories and describe the structure of the modules sent to zero. Taking coefficients in a semi-simple Artinian ring, we deduce that the Witt group of Seifert forms is isomorphic to the Witt group of Blanchfield-Duval forms.
77 pages, LaTeX. One figure compiles with dratex.sty (package included). This version has minor corrections
77 pages, LaTeX. One figure compiles with dratex.sty (package included). This version has minor corrections