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Topologically transitive homeomorphisms of quotients of tori

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  • This paper considers the following question: for what finite subgroups $G\subset GL(n, \mathbb Z)$, does there exist an element $A\in GL(n, \mathbb Z)$ inducing a topologically transitive homeomorphism of $T^n$/$G$ We show that for $n = 2$ and 3, the only possibility is $G =\{\pm I\}$. Curiously, in higher dimension the structure is less restrictive. We give a variety of examples in dimension 4. Nevertheless, we show that in dimension $\geq 4$, there are relatively few irreducible examples.
    Mathematics Subject Classification: 54H20, 57S25.


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