Formality properties of finitely generated groups and Lie algebras
-
Alexander I. Suciu
und
He Wang
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.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1010298
Funding source: National Security Agency
Award Identifier / Grant number: H98230-13-1-0225
Funding source: Simons Foundation
Award Identifier / Grant number: 354156
Funding statement: The first author was supported in part by the National Science Foundation (grant DMS-1010298), the National Security Agency (grant H98230-13-1-0225), and the Simons Foundation (collaboration grant for mathematicians 354156).
Acknowledgements
We wish to thank Yves Cornulier, Ştefan Papadima, and Richard Porter for several useful comments regarding this work.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Characteristic functions of semigroups in semi-simple Lie groups
- Damping estimates for oscillatory integral operators with real-analytic phases and its applications
- Formality properties of finitely generated groups and Lie algebras
- Toric actions in cosymplectic geometry
- On classification of typical representations for GL3(F)
- Integrable generators of Lie algebras of vector fields on ℂn
- Expanding phenomena over matrix rings
- On sup-norm bounds part II: GL(2) Eisenstein series
- Sublinear elliptic problems under radiality. Harmonic NA groups and Euclidean spaces
- Partial and full boundary regularity for non-autonomous functionals with Φ-growth conditions
- Radial averaging operator acting on Bergman and Lebesgue spaces
- The 𝑝-adic variation of the Gross–Kohnen–Zagier theorem
Artikel in diesem Heft
- Frontmatter
- Characteristic functions of semigroups in semi-simple Lie groups
- Damping estimates for oscillatory integral operators with real-analytic phases and its applications
- Formality properties of finitely generated groups and Lie algebras
- Toric actions in cosymplectic geometry
- On classification of typical representations for GL3(F)
- Integrable generators of Lie algebras of vector fields on ℂn
- Expanding phenomena over matrix rings
- On sup-norm bounds part II: GL(2) Eisenstein series
- Sublinear elliptic problems under radiality. Harmonic NA groups and Euclidean spaces
- Partial and full boundary regularity for non-autonomous functionals with Φ-growth conditions
- Radial averaging operator acting on Bergman and Lebesgue spaces
- The 𝑝-adic variation of the Gross–Kohnen–Zagier theorem
