Spectral rigidity of group actions: Applications to the case gr⟨𝑡,𝑠;𝑡𝑠=𝑠𝑡²⟩

Ageev, Oleg

doi:10.1090/S0002-9939-05-08380-2

Spectral rigidity of group actions: Applications to the case $\mbox {gr}\langle t,s ; ts=st^2\rangle$
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Abstract:

We apply a technique to study the notion of spectral rigidity of group actions to a group $\mbox {gr}\langle t,s ; \ ts=st^2\rangle$. As an application, we prove that there exist rank one weakly mixing transformations conjugate to its square, thereby giving a positive answer to a well-known question.

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