Relative K-theory with applications to factor groupoids

Abstract: In this talk I will speak about a portrait of relative K-theory for C*-algebras inspired by a setup due to Max Karoubi using Banach categories. After presenting some useful exact sequences, I will show how the portrait gives the same data, although through a different lens, as the K-groups that arise from the mapping cone construction. After this, I will present some examples of C*-algebras from factor groupoids whose K-theory data are computable (in fact, controllable, to a certain degree) using these relative K-theory tools.

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.