The Heisenberg group is pan-rational

DOI10.1016/j.aim.2019.01.046zbMath1504.20043OpenAlexW2911726904WikidataQ128491115 ScholiaQ128491115MaRDI QIDQ1731562

Michael Shapiro, Moon Duchin

Publication date: 13 March 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2019.01.046

zbMATH Keywords

Heisenberg groupgrowth of groups

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Nilpotent groups (20F18) Asymptotic properties of groups (20F69)

Related Items

Equations in virtually abelian groups: Languages and growth ⋮ Growth in higher Baumslag-Solitar groups ⋮ Asymptotic behavior of the Riemannian Heisenberg group and its horoboundary ⋮ Growth of unbounded sets in nilpotent groups and random mapping statistics ⋮ Conjugacy growth in the higher Heisenberg groups ⋮ Unnamed Item ⋮ Rational growth in virtually abelian groups ⋮ Rational growth in torus bundle groups of odd trace

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometry of locally compact groups of polynomial growth and shape of large balls
• A geometric approach to the almost convexity and growth of some nilpotent groups
• The rationality of the Poincaré series associated to the p-adic points on a variety
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• On isoperimetric inequalities in Minkowski spaces
• The combinatorial structure of cocompact discrete hyperbolic groups
• Almost convex groups
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Growth series of finite extensions of \(Z^ n \)are rational
• Growth in higher Baumslag-Solitar groups
• Automatic structures, rational growth, and geometrically finite hyperbolic groups
• Rational and transcendental growth series for the higher Heisenberg groups
• On problems related to growth, entropy, and spectrum in group theory
• Integrability of oscillatory functions on local fields: transfer principles
• Classification of subdivision rules for geometric groups of low dimension
• Fine asymptotic geometry in the Heisenberg group
• Fall Sampler: Counting in Groups: Fine Asymptotic Geometry
• Croissance polynomiale et périodes des fonctions harmoniques
• Croissance des boules et des géodésiques fermées dans les nilvariétés
• Model Theory
• On the rate of convergence to the asymptotic cone for nilpotent groups and subFinsler geometry
• The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups
• The Isoperimetric Problem in the Minkowski Plane