Taylor expansions of groups and filtered-formality

Suciu, Alexander I.; Wang, He

doi:10.1007/s40879-019-00389-6

Cited by 4 publications

(5 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Related results for the McCool groups (or, the welded pure braid groups) and other braid-like groups are given in [76,78]. Finally, the relationship between filtered formality and expansions of groups is explored in [79].…”

Section: 5mentioning

confidence: 99%

Formality properties of finitely generated groups and Lie algebras

Suciu

Wang

2019

Forum Mathematicum

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: 5mentioning

confidence: 99%

Formality properties of finitely generated groups and Lie algebras

Suciu

Wang

2019

Forum Mathematicum

Self Cite

View full text Add to dashboard Cite

show abstract

“…A weaker condition was given in [132]: we say that is filtered formal if ( ) is the completion of gr( , Q) with respect to its LCS filtration. As shown in [133], this condition is equivalent to the existence of a Taylor expansion, → gr(Q[ ]).…”

Section: Malcev and Holonomy Lie Algebrasmentioning

confidence: 99%

“…). Definition 6.1 ([8], [133]). An expansion : → gr(Q[ ]) is called a Taylor expansion if it sends each element of to a group-like element of gr(…”

Section: Multiplicative Expansions and Taylor Expansionsmentioning

confidence: 99%

See 1 more Smart Citation

Formality and finiteness in rational homotopy theory

Suciu¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…For more on this topic, we refer to [20,25,45,49,70,72]. We will only recall here two results which will prove to be useful to us.…”

Section: Holonomy Lie Algebras and Formality Propertiesmentioning

confidence: 99%

Alexander invariants and cohomology jump loci in group extensions

Suciu

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We study the integral, rational, and modular Alexander invariants, as well as the cohomology jump loci of groups arising as extensions with trivial algebraic monodromy. Our focus is on extensions of the form 1→K→G→Q→1, where Q is an abelian group acting trivially on H1(K;ℤ), with suitable modifications in the rational and mod-p settings. We find a tight relationship between the Alexander invariants, the characteristic varieties, and the resonance varieties of the groups K and G. This leads to an inequality between the respective Chen ranks, which becomes an equality in degrees greater than 1 for split extensions.

show abstract

Taylor expansions of groups and filtered-formality

Cited by 4 publications

References 46 publications

Formality properties of finitely generated groups and Lie algebras

Formality properties of finitely generated groups and Lie algebras

Formality and finiteness in rational homotopy theory

Alexander invariants and cohomology jump loci in group extensions

Contact Info

Product

Resources

About