Accessibilité hiérarchique des groupes de présentation finie

Delzant, Thomas; Potyagailo, Leonid

doi:10.1016/s0040-9383(99)00078-6

Cited by 21 publications

(46 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If we weaken the assumption "π is the fundamental group of a finite aspherical cell complex" to "π is finitely presented", then the same conclusion holds without the word "tangentially". Any manifold of constant sectional curvature has zero rational Pontrjagin classes [Ave70], hence, applying the Mayer-Vietoris sequence and the accessibility result of Delzant and Potyagailo [DP98] (reviewed in 2.5), we deduce the following. Theorem 1.2.…”

Section: Introductionmentioning

confidence: 89%

See 1 more Smart Citation

Pinching, Pontrjagin classes, and negatively curved vector bundles

Belegradek¹

2001

Invent. math.

View full text Add to dashboard Cite

We prove several finiteness results for the class M a,b,π,n of n-manifolds that have fundamental groups isomorphic to π and that can be given complete Riemannian metrics of sectional curvatures within [a, b] where a ≤ b < 0 . In particular, if M is a closed negatively curved manifold of dimension at least three, then only finitely many manifolds in the class M a,b,π1(M),n are total spaces of vector bundles over M . Furthermore, given a word-hyperbolic group π and an integer n there exists a positive ǫ = ǫ(n, π) such that the tangent bundle of any manifold in the class M −1−ǫ,−1,π,n has zero rational Pontrjagin classes.

show abstract

Section: Introductionmentioning

confidence: 89%

“…The definition 2.9 and the theorem 2.10 are taken from [DP98]. I am grateful to Thomas Delzant for helpful discussions.…”

Section: Accessibility Over Virtually Nilpotent Groupsmentioning

confidence: 99%

Pinching, Pontrjagin classes, and negatively curved vector bundles

Belegradek¹

2001

Invent. math.

View full text Add to dashboard Cite

show abstract

“…In [6], Delzant and Potyagailo proved a very general strong accessibility result. They showed that any finitely presented group without 2-torsion admits a finite hierarchy over any family of "elementary" subgroups (see Definition 7).…”

Section: Introductionmentioning

confidence: 93%

“…Firstly, a hierarchy from [6] is over one fixed family of subgroups. For this result, however, we alternate between decomposing over finite subgroups and two-ended subgroups.…”

Section: Introductionmentioning

confidence: 99%

Strong accessibility for hyperbolic groups

Vavrichek

2008

Algebr. Geom. Topol.

View full text Add to dashboard Cite

show abstract

“…To finish our historical discussion let us point out that the relative invariant T (G, E) allows one to prove the accessibility of a finitely presented group G without 2-torsion over elementary subgroups [DePo1]. Using these methods it was shown recently that for hyperbolic groups without 2-torsion any canonical hierarchy over finite subgroups and one-ended subgroups is finite [Va].…”

mentioning

confidence: 99%