Dynamical comparison of amenable actions by non-amenable groups.

Abstract: We pull back boundary-type actions to paradoxical decompositions of the acting group itself. In particular, we obtain strong paradoxical structure in non-elementary hyperbolic groups, in many lattices in Lie groups, and in non-elementary Baumslag-Solitar groups. This allows us to show that whenever such groups admit a minimal amenable topologically free action on a compact Hausdorff space, the system has dynamical comparison and the attached crossed product is a purely infinite classifiable C*-algebra.

This is joint work with Eusebio Gardella, Julian Kranz, and Petr Naryshkin.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

---

Noncommutative Geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click sju.webex.com/meet/nikolaei (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

---