Invariants of Boundary Link Cobordism II. The Blanchfield-Duval Form

Details Invariants of Boundary Link Cobordism II. The Blanchfield-Duval Form Invariants of Boundary Link Cobordism II. The Blanchfield-Duval Form

2004-04-12

arxiv.org/abs/math/0404229v2

Mathematics

Algebraic Topology

77 pages, LaTeX. One figure compiles with dratex.sty (package included). This version has minor corrections

Scientific paper

We use the Blanchfield-Duval form to define complete invariants for the cobordism group C_{2q-1}(F_\mu) of (2q-1)-dimensional \mu-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 \mu-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.

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