solvable fundamental group
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scholarly journals Partial hyperbolicity and classification: a survey

2016 ◽  
Vol 38 (2) ◽  
pp. 401-443 ◽  
Author(s):  
ANDY HAMMERLINDL ◽  
RAFAEL POTRIE
Keyword(s):  
Fundamental Group ◽  
Three Dimensional ◽  
Group Classification ◽  
Partial Hyperbolicity ◽  
Hyperbolic Diffeomorphisms ◽  
Higher Dimensional ◽  
Partially Hyperbolic ◽  
Anosov Flows ◽  
Partially Hyperbolic Diffeomorphisms ◽  
Solvable Fundamental Group

This paper surveys recent results on classifying partially hyperbolic diffeomorphisms. This includes the construction of branching foliations and leaf conjugacies on three-dimensional manifolds with solvable fundamental group. Classification results in higher-dimensional settings are also discussed. The paper concludes with an overview of the construction of new partially hyperbolic examples derived from Anosov flows.

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