2015/08/06 by Darren Creutz, Creutz, Darren
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.DS
paper · pdf · doi:10.48550/arxiv.1508.01561
arXiv admin note: substantial text overlap with arXiv:1303.3949
openalex publication_date 2015/08/06 · arxiv created 2016/03/26 · arxiv updated 2016/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an exposition of contractive spaces and of relatively contractive maps. Contractive spaces are the natural opposite of measure-preserving actions and relatively contractive maps the natural opposite of relatively measure-preserving maps. These concepts play a central role in the work of the author and J.~Peterson on the rigidity of actions of semisimple groups and their lattices and have also appeared in recent work of various other authors. We present detailed definitions and explore the relationship of these phenomena with other aspects of the ergodic theory of group actions, proving along the way several new results, with an eye towards explaining how contractiveness is intimately connected with rigidity phenomena.