The structure theory of nilspaces. III: Inverse limit representations and topological dynamics

DOI10.1016/j.aim.2020.107059zbMath1437.37011arXiv1605.08950OpenAlexW3008191036MaRDI QIDQ2308312

Yonatan Gutman, Freddie Manners, Péter Pál Varjú

Publication date: 2 April 2020

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

Full work available at URL: https://arxiv.org/abs/1605.08950

zbMATH Keywords

Lie groupnilmanifoldproximal relationnilspacefinite order system

Mathematics Subject Classification ID

Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Local Lie groups (22E05) Dynamics in general topological spaces (37B02)

Related Items (15)

Approximately symmetric forms far from being exactly symmetric ⋮ Regularity and inverse theorems for uniformity norms on compact abelian groups and nilmanifolds ⋮ The structure theory of nilspaces. I ⋮ Maximal pronilfactors and a topological Wiener-Wintner theorem ⋮ On higher-order Fourier analysis in characteristic p ⋮ On the structure theory of cubespace fibrations ⋮ Nilspace Factors for General Uniformity Seminorms, Cubic Exchangeability and Limits ⋮ Host–Kra theory for -systems and multiple recurrence ⋮ Directional dynamical cubes for minimal -systems ⋮ The structure theory of Nilspaces II: Representation as nilmanifolds ⋮ http://discreteanalysisjournal.com/article/2105-notes-on-nilspaces-algebraic-aspects ⋮ Notes on compact nilspaces ⋮ Combinatorial properties of Nil-Bohr sets ⋮ On nilspace systems and their morphisms ⋮ Strictly ergodic distal models and a new approach to the Host-Kra factors

Cites Work

• The Möbius function is strongly orthogonal to nilsequences
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• Nilsequences and a structure theorem for topological dynamical systems
• Linear equations in primes
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• Multiple recurrence and nilsequences (with an appendix by Imre Ruzsa)
• The structure theory of nilspaces. I
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• Homomorphisms of Transformation Groups
• Compact Lie Groups
• Universal characteristic factors and Furstenberg averages
• Nilsystèmes d’ordre 2 et parallélépipèdes
• Parallelepipeds, nilpotent groups and Gowers norms
• The structure theory of Nilspaces II: Representation as nilmanifolds
• http://discreteanalysisjournal.com/article/2105-notes-on-nilspaces-algebraic-aspects
• Notes on compact nilspaces
• Spaces With a Compact Lie Group of Transformations
• An inverse theorem for the Gowers \(U^{s+1}[N\)-norm]
• Lie groups beyond an introduction
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