Formal computations in low-dimensional topology: Links and group presentations. (English) Zbl 0807.55008

Markl, Martin

Bureš, J. (ed.) et al., The proceedings of the 11th winter school on geometry and physics held in Srní, Czechoslovakia, January 5-12, 1991. Palermo: Circolo Matematico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 30, 125-131 (1993).

The author describes the moduli space of Sullivan models of 2-skeletal spaces and complements of links as quotients of spaces of derivations of finitely generated free Lie algebras \(L\) by the action of a subgroup of automorphisms of \(L\). For recall, a 2-skeletal space is a path connected space \(S\) satisfying \(H^{\geq 3} (S;\mathbb{Q}) = 0\) and \(\dim H^* (S, \mathbb{Q}) < \infty\). The paper contains as an application a complete description of the Lie algebras associated to the fundamental groups of complements of two-component links in terms of their Milnor numbers.
For the entire collection see [Zbl 0777.00026].

Reviewer: Y.Felix (Louvain-La-Neuve)

MSC:

55P62	Rational homotopy theory
57M25	Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

moduli space of Sullivan models of 2-skeletal spaces; complements of links; spaces of derivations of finitely generated free Lie algebras; two-component links; Milnor numbers