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All groups are surjunctive
- Publication Year :
- 2019
-
Abstract
- We prove that for any finitely generated group $G$ and any $k\geq1$, 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.<br />Comment: 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
- Subjects :
- Mathematics - Dynamical Systems
Mathematics - Group Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1912.00541
- Document Type :
- Working Paper