Topologically unrealizable automorphisms of free groups
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- by John R. Stallings PDF
- Proc. Amer. Math. Soc. 84 (1982), 21-24 Request permission
Abstract:
Let $\phi :F \to F$ be an automorphism of a finitely generated free group. It has been conjectured (I heard it from Peter Scott) that the fixed subgroup of $\phi$ is always finitely generated. This is known to be so if $\phi$ has finite order [1], or if $\phi$ is realizable by a homeomorphism of a compact $2$-manifold with boundary [2]. Here we give examples of automorphisms $\phi$, no power of which is topologically realizable on any $2$-manifold; perhaps the simplest is the automorphism of the free group of rank 3, given by $\phi (x) = y$, $\phi (y) = z$, $\phi (z) = xy$.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 21-24
- MSC: Primary 20E05; Secondary 57M99
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633269-8
- MathSciNet review: 633269