Abstract
We explore the graded-formality and filtered-formality properties of
finitely generated groups by studying the various Lie algebras
over a field of characteristic 0 attached to such groups, including
the Malcev Lie algebra, the associated graded Lie algebra,
the holonomy Lie algebra, and the Chen Lie algebra.
We explain how these notions behave with
respect to split injections, coproducts, direct products, as well as field
extensions, and how they are inherited by solvable and nilpotent quotients.
A key tool in this analysis is the 1-minimal model of the group, and
the way this model relates to the aforementioned Lie algebras.
We illustrate our approach with examples drawn
from a variety of group-theoretic and topological contexts, such
as finitely generated torsion-free nilpotent
groups, link groups, and fundamental groups of Seifert fibered manifolds.