Tuesday, September 1, 2020

Gernot Greschonig on Rechtsaktion (Right Action) and Linksaktion (Left Action) in Topological Dynamics

Gernot Greschonig  writes:

I remember that once Joe made a statement to me like “politically I started left from the center and I always kept moving to the left”. Taking this into account, it might be surprising that Joe’s wonderful book on “Minimal Flows and their Extensions” is written in the mathematical notation of right actions. However, this notation was common at least until the end of the 70s, and it might be considered to be according to the political attitudes of some of the founders of Topological Dynamics. Although (politically) the world might not have changed into the right (-> left) direction, nowadays everybody writes in the notation of left actions. Mathematically this is just a more or less trivial change of notation, however the notation has to be maintained consequently throughout a lecture to aviod confusion among the students. 

 Some time ago I gave a lecture on the topic at the Technical University in Vienna, therefore I had to prepare some notes, just translations into a different language (German) and a different mathematical notation (left actions). The outcome (some unofficial, unpublished lecture notes of translations of copyrighted material out of the book!)  is in the essay "Auszuge aus Minimal Flows and Their Extensions\ von Joseph Auslander, Kapitel 1{7,Verlag North-Holland 1988."

  I want to finish with expression of my gratefulness for Joe’s outstanding exposition of Topological Dynamics.
 

 

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