$L^2$-Betti numbers and computability of reals

Abstract: For several real-valued invariants from topology or group theory, the individual values are not arbitray real numbers, but (right-)computable reals. For example, the real numbers arising as $L^2$-Betti numbers of groups are right-computable, where the right-computability degree is bounded by the Turing degree of the word problem.

I will give an overview of such results on $L^2$-Betti numbers and related invariants. This talk is based on joint work with Matthias Uschold.

logic

Audience: researchers in the topic

( paper )

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Computability theory and applications

Series comments: Description: Computability theory, logic

The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.

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