Smale spaces and their dimension theory

Abstract: Smale spaces were defined by David Ruelle in the 1970's as topological models for the typically fractal-like hyperbolic nonwandering sets of Stephen Smale's Axiom A systems. A Smale space is a compact metric space together with a homeomorphism having exponential contraction and expansion behaviour. Prototype examples are the topological Markov chains, aperiodic substitution tilings and hyperbolic toral automorphisms. This talk will give an example-driven introduction to Smale spaces with a focus on their dimension theory, which can be studied via Markov partitions and Ahlfors regular measures. If time permits, I will briefly mention how the dimension theory of a Smale space is related to fine analytic properties of the operator algebras encoding the stable and unstable foliations on it.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides | video )

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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 meet.google.com/zjd-ehrs-wtx (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.

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