The Topology of Compact Lie Group Actions Through the Lens of Finite Models

Papadima, Ştefan; Suciu, Alexander I.

doi:10.1093/imrn/rnx294

Cited by 12 publications

(20 citation statements)

References 49 publications

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“…Hence, we will sometimes avoid mentioning the coefficient field when referring to these formality notions. The descent property for partial formality from Theorem 1.2, part (1) has been used in [62] to establish the (n − 1)-formality over Q of compact Sasakian manifolds of dimension 2n + 1.…”

Section: Formality Notionsmentioning

confidence: 99%

Formality properties of finitely generated groups and Lie algebras

Suciu

Wang

2019

Forum Mathematicum

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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.

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Section: Formality Notionsmentioning

confidence: 99%

Formality properties of finitely generated groups and Lie algebras

Suciu

Wang

2019

Forum Mathematicum

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“…We conclude with one more class of spaces and maps where Corollary 6.5 applies. 28 STEFAN PAPADIMA AND ALEXANDER I. SUCIU Proposition 6.8. Let f : X Ñ X 1 be a pq´1q-connected map between q-finite, pointed spaces, for some q ě 1.…”

Section: 2mentioning

confidence: 99%

Naturality properties and comparison results for topological and infinitesimal embedded jump loci

Papadima

Suciu

2019

Advances in Mathematics

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We use augmented commutative differential graded algebra (acdga) models to study G-representation varieties of fundamental groups π " π 1 pMq and their embedded cohomology jump loci, around the trivial representation 1. When the space M admits a finite family of maps, uniformly modeled by acdga morphisms, and certain finiteness and connectivity assumptions are satisfied, the germs at 1 of Hompπ, Gq and of the embedded jump loci can be described in terms of their infinitesimal counterparts, naturally with respect to the given families. This approach leads to fairly explicit answers when M is either a compact Kähler manifold, the complement of a central complex hyperplane arrangement, or the total space of a principal bundle with formal base space, provided the Lie algebra of the linear algebraic group G is a non-abelian subalgebra of sl 2 pCq.

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“…(3) The inclusion (1.6) is an equality, for some convenient compactification of M. This theorem, which will be proved in § 7.2, provides a topological interpretation for [22,Question 8.4], which asks whether statement (4) from above always holds.…”

Section: Topological Versus Infinitesimal Factorizationsmentioning

confidence: 99%

“…We denote by ϕ : H → A the canonical cdga inclusion. Note that both H and A are cdgas with positive weights, preserved by the map ϕ; see [22,Proposition 9.1].…”

Section: Rank Greater Thanmentioning

confidence: 99%

Rank Two Topological and Infinitesimal Embedded Jump Loci of Quasi-Projective Manifolds

Papadima¹,

Suciu²

2018

J. Inst. Math. Jussieu

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We study the germs at the origin of G-representation varieties and the degree 1 cohomology jump loci of fundamental groups of quasi-projective manifolds. Using the Morgan-Dupont model associated to a convenient compactification of such a manifold, we relate these germs to those of their infinitesimal counterparts, defined in terms of flat connections on those models. When the linear algebraic group G is either SL 2 pCq or its standard Borel subgroup and the depth of the jump locus is 1, this dictionary works perfectly, allowing us to describe in this way explicit irreducible decompositions for the germs of these embedded jump loci. On the other hand, if either G " SL n pCq for some n ě 3, or the depth is greater than 1, then certain natural inclusions of germs are strict.

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The Topology of Compact Lie Group Actions Through the Lens of Finite Models

Cited by 12 publications

References 49 publications

Formality properties of finitely generated groups and Lie algebras

Formality properties of finitely generated groups and Lie algebras

Naturality properties and comparison results for topological and infinitesimal embedded jump loci

Rank Two Topological and Infinitesimal Embedded Jump Loci of Quasi-Projective Manifolds

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