All groups are surjunctive
Dynamical Systems
2019-12-06 v2 Group Theory
Abstract
We prove that for any finitely generated group and any , the space of -colorings of does not admit a strict self-embedding. This settles the Gottschalk surjunctivity conjecture and, consequently, Kaplansky's direct finiteness conjecture.
Cite
@article{arxiv.1912.00541,
title = {All groups are surjunctive},
author = {Jan Cannizzo},
journal= {arXiv preprint arXiv:1912.00541},
year = {2019}
}
Comments
As several people have pointed out to me, the last sentence of Lemma 5.3 is not justified. This likely counts as a fatal flaw that invalidates the main theorem (Theorem 5.4). I would like to thank those who took the time to read the preprint and send me their feedback. I hereby retract the claimed result