Rank gradient, cost of groups and the rank versus Heegaard genus problem
By Miklós Abért, Nikolay Nikolov. 2007
102 citations recorded by the source corpus.
We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the `Rank vs. Heegaard genus' conjecture on hyperbolic 3-manifolds is incompatible with the `Fixed Price problem' in topological dynamics.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/59e543153041096953500f2f6f9584401315fddb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Expander graphs in pure and applied mathematics (2011, background): “zero). Gaboriau proved this conjecture for various groups but it is still widely open for general . An interesting example in which the cost was computed explicitly is: 55 Theorem 6.17 (Abert-Nikolov [AN]). Let be a nitely generated group, L= fN ig i2Na chain of nite index normal subgroups N 1 N 2 ”
- Topological stability and pseudo-orbit tracing property of group actions (2016, background): “Profinite actions have been studied extensively in rank gradient, orbit equivalence, operator algebras, and sofic entropy theory [2, 5, 7].”