Abstract
We consider an algebraic parametrization for the set of (Mal'cev completed) fundamental groups of the spaces with fixed first two Betti numbers, having in mind applications in low-dimensional topology and especially in link theory. The factor set of (restricted) isomorphism types of these groups acquires the structure of a ‘moduli space’, giving rise to invariants which, in the case of links, detect the isotopy type. We indicate two methods of computation for these invariants. We also prove a rigidity result for the associated graded Lie algebra of the fundamental group. A lot of examples are given.
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