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

Abstract

We study the computability degree of real numbers arising as $L^2$-Betti numbers or $L^2$-torsion of groups, parametrised over the Turing degree of the word problem.

arXiv comment33 pages; To appear in Computability; v2: clarified Theorem 1.5; v3: removed Section 9, minor corrections; v4: added Appendix B and Remark 1.5; Lean implementation available at https://gitlab.com/L2-comp/l2-comp-lean;