Dynamic asymptotic dimension and homology

Abstract: Groupoid homology has attracted increasing attention from from the topological dynamics and operator algebras communities following the work of Matui. Matui's HK conjecture predicts that the K-theory groups of the reduced C*-algebra of a minimal essentially principal ample groupoid coincides with its homology groups. We prove that homology of principal ample groupoids vanish in degree above its dynamical asymptotic dimension, a notion of dimension from topological dynamics. We deduce several consequences: Matui's HK conjecture holds for low dimensional principal ample groupoids, and classification of their reduced C*-algebra. (Joint work with Christian Bonicke, Jamie Gabe and Rufus Willett)

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( 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.