Rank gradient, cost of groups and the rank versus Heegaard genus problem

DOI10.4171/JEMS/344zbMath1271.57046arXivmath/0701361MaRDI QIDQ713961

Nikolay Nikolov, Miklós Abért

Publication date: 19 October 2012

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701361

zbMATH Keywords

costrank gradientHeegaard genusfixed price

Mathematics Subject Classification ID

Related Items (40)

Growth of mod-2 homology in higher-rank locally symmetric spaces ⋮ Integral foliated simplicial volume and \(S^1\)-actions ⋮ Torsion homology growth in arithmetic groups ⋮ Rank Gradient andp-gradient of Amalgamated Free Products and HNN Extensions ⋮ Approximating \(L^2\)-invariants and homology growth ⋮ Ascending chains of finitely generated subgroups ⋮ Asymptotic invariants of lattices in locally compact groups ⋮ On a curious problem and what it lead to ⋮ On computing homology gradients over finite fields ⋮ On profinite groups with positive rank gradient ⋮ Groups not presentable by products. ⋮ Presentability by products for some classes of groups ⋮ Point processes, cost, and the growth of rank in locally compact groups ⋮ Schreier’s formula for prosupersolvable groups ⋮ Some topics in the dynamics of group actions on rooted trees. ⋮ On the linearity of lattices in affine buildings and ergodicity of the singular Cartan flow ⋮ Invariant means and the structure of inner amenable groups ⋮ Sofic boundaries of groups and coarse geometry of sofic approximations ⋮ The rank gradient from a combinatorial viewpoint. ⋮ Pro‐p groups of positive rank gradient and Hausdorff dimension ⋮ Integral foliated simplicial volume of aspherical manifolds ⋮ Rank gradient versus stable integral simplicial volume ⋮ Volume gradients and homology in towers of residually-free groups ⋮ The \(L^2\)-torsion polytope of amenable groups ⋮ Weak containment in the space of actions of a free group ⋮ Rank and genus of 3-manifolds ⋮ Rank gradient and cost of Artin groups and their relatives. ⋮ Rank gradient in co-final towers of certain Kleinian groups ⋮ On the rigidity of rank gradient in a group of intermediate growth ⋮ Cost vs. integral foliated simplicial volume ⋮ Ranks of subgroups in boundedly generated groups ⋮ Uniform rank gradient, cost, and local-global convergence ⋮ Weak containment of measure-preserving group actions ⋮ A spectral strong approximation theorem for measure-preserving actions ⋮ Combinatorial cost: A coarse setting ⋮ Integral approximation of simplicial volume of graph manifolds ⋮ Expander graphs in pure and applied mathematics ⋮ Non-standard limits of graphs and some orbit equivalence invariants ⋮ Kazhdan groups have cost 1 ⋮ Topological stability and pseudo-orbit tracing property of group actions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The rank gradient from a combinatorial viewpoint.
• Heegaard genus of closed orientable Seifert 3-manifolds
• On the geometric and the algebraic rank of graph manifolds
• Bounds for multiplicities of automorphic representations
• Stabilizers for ergodic actions of higher rank semisimple groups
• Geometry of growth: approximation theorems for \(L^2\) invariants
• Weak containment in the space of actions of a free group
• Expanders, rank and graphs of groups
• \(\ell^2\) invariants of equivalence relations and groups
• Asymptotics of Betti numbers, \(l^ 2\)-invariants and laminations
• Topics in orbit equivalence
• A non-Haken hyperbolic 3-manifold covered by a surface bundle
• Cost of equivalence relations and groups
• Heegaard splittings, the virtually Haken conjecture and property \((\tau)\)
• Eigenvalues of the Laplacian, the first Betti number and the congruence subgroup problem
• Generations for arithmetic groups.
• A -group with positive rank gradient
• Rank gradient and torsion groups
• SYMMETRIC GROUPS AS PRODUCTS OF ABELIAN SUBGROUPS
• Dimension and randomness in groups acting on rooted trees
• Criteria for virtual fibering
• On the cost of generating an equivalence relation
• Bernoulli actions are weakly contained in any free action
• Hyperbolic volume, Heegaard genus and ranks of groups
• On the Number of Generators of a Free Product

This page was built for publication: Rank gradient, cost of groups and the rank versus Heegaard genus problem