English

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

Group Theory 2023-03-08 v4 Logic in Computer Science Geometric Topology Logic

Abstract

We study the computability degree of real numbers arising as L2L^2-Betti numbers or L2L^2-torsion of groups, parametrised over the Turing degree of the word problem.

Cite

@article{arxiv.2202.03159,
  title  = {$L^2$-Betti numbers and computability of reals},
  author = {Clara Loeh and Matthias Uschold},
  journal= {arXiv preprint arXiv:2202.03159},
  year   = {2023}
}

Comments

33 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;