Fixed subsets of homomorphisms of free groups
We derive a bound for the rank of the fixed point set Fp(α) of a monomorphism α and the fixed point group Fix(α) of homomorphisms α of subgroups G of a free group F into F. We do not require the ranks of G and F to be finite; these conditions are replaced by a finiteness condition for α.
KeywordsFree Group Initial Segment Cayley Graph Unoriented Edge Infinite Path
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- M. Bestvina and M. Handel, Train Tracks and Automorphisms of Free Groups, manuscript Google Scholar
- S. M. Gersten, Fixed points of automorphisms of free groups, Adv. Math. 84 (1986) 91–119Google Scholar
- W. Imrich, S. Krstić and E. C. Turner, On the rank of fixed point sets of automorphisms of free groups, Cycles and Rays NATO ASI Ser. C, Kluwer Academic Publishers, Dordrecht (1990), 113–122Google Scholar
- J. R. Stallings, Graphical Theory of Automorphisms of Free Groups, Combinatorial Group Theory and Topology, 79–105, Annals of Mathematical Studies 111, Princeton University Press, Princeton, N.J. 1987Google Scholar