All groups are surjunctive

Abstract

We prove that for any finitely generated group $G$ and any $k\ge 1$, the space of $k$-colorings of $G$ does not admit a strict self-embedding. This settles the Gottschalk surjunctivity conjecture and, consequently, Kaplansky's direct finiteness conjecture.

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