  An n-dimensional \mu-component boundary link is a codimension 2 embedding of
spheres L=\bigsqcup_{\mu}S^n \subset S^{n+2} such that there exist \mu disjoint
oriented embedded (n+1)-manifolds which span the components of L. An F_\mu-link
is a boundary link together with a cobordism class of such spanning manifolds.
The F_\mu-link cobordism group C_n(F_\mu) is known to be trivial when n is even
but not finitely generated when n is odd.
  Our main result is an algorithm to decide whether two odd-dimensional
F_\mu-links represent the same cobordism class in C_{2q-1}(F_\mu) assuming q>1.
We proceed to compute the isomorphism class of C_{2q-1}(F_\mu), generalizing
Levine's computation of the knot cobordism group C_{2q-1}(F_1).
  Our starting point is the algebraic formulation of Levine, Ko and Mio who
identify C_{2q-1}(F_\mu) with a surgery obstruction group, the Witt group
G^{(-1)^q,\mu}(Z) of \mu-component Seifert matrices. We obtain a complete set
of torsion-free invariants by passing from integer coefficients to complex
coefficients and by applying the algebraic machinery of Quebbemann, Scharlau
and Schulte. Signatures correspond to `algebraically integral' simple self-dual
representations of a certain quiver (directed graph with loops). These
representations, in turn, correspond to algebraic integers on an infinite
disjoint union of real affine varieties.
  To distinguish torsion classes, we consider rational coefficients in place of
complex coefficients, expressing G^{(-1)^q,\mu}(Q) as an infinite direct sum of
Witt groups of finite-dimensional division Q-algebras with involution.
Numerical invariants of such Witt groups are available in the literature.

Algebraic Topology;Representation Theory