Efficient representatives for automorphisms of free products.

Collins, Donald J.; Turner, Edward C.

doi:10.1307/mmj/1029005072

Cited by 29 publications

(47 citation statements)

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“…This improved the result of CollinsTurner in [8] about the Scott conjecture for these groups, and provided an alternative proof of Theorem 5.7 for the free case. The arguments used are in the line of the Bestvina-Handel theory.…”

Section: Dicks and E Ventura In [14]supporting

confidence: 61%

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Fixed subgroups in free groups: a survey

Capell¹

2002

Contemporary Mathematics

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Section: Dicks and E Ventura In [14]supporting

confidence: 61%

“…In 1994, D. Collins and E. Turner published [8]. Here, the authors reworked the whole Bestvina-Handel theory in a more general context, to obtain the same result for a larger class of groups.…”

Section: Fixed Subgroups After Bestvina-handelmentioning

confidence: 86%

Fixed subgroups in free groups: a survey

Capell¹

2002

Contemporary Mathematics

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“…We argue by induction on the Kurosh rank r(G) = p + q. The relative train track maps of Bestvina and Handel [3] have been generalized to free products in [5], so that we can represent anyα ∈ Out(G) by a relative train track map ϕ: X → X. We assume thatα has finite order, and we use ϕ to construct an α-invariant splitting of G.…”

Section: Groups With Infinitely Many Endsmentioning

confidence: 99%

Automorphisms of Hyperbolic Groups and Graphs of Groups

Levitt

2005

Geom Dedicata

137

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Using the canonical JSJ splitting, we describe the outer automorphism group Out(G) of a one-ended word hyperbolic group G. In particular, we discuss to what extent Out(G) is virtually a direct product of mapping class groups and a free abelian group, and we determine for which groups Out(G) is infinite. We also show that there are only finitely many conjugacy classes of torsion elements in Out(G), for G any torsion-free hyperbolic group. More generally, let be a finite graph of groups decomposition of an arbitrary group G such that edge groups G e are rigid (i.e. Out(G e ) is finite). We describe the group of automorphisms of G preserving , by comparing it to direct products of suitably defined mapping class groups of vertex groups.

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“…Goldstein and Turner extended it to monomorphisms of free groups [11], and later to arbitrary endomorphisms [12]. Collins and Turner extended it to automorphisms of free products of freely indecomposable groups [3] (see the survey by Ventura [22]). With respect to automorphisms, the widest generalization is to hyperbolic groups and is due to Paulin [15].…”

Section: Introductionmentioning

confidence: 99%

Fixed points of endomorphisms of virtually free groups

Silva

2013

Pacific J. Math.

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A fixed point theorem is proved for inverse transducers, leading to an automatatheoretic proof of the fixed point subgroup of an endomorphism of a finitely generated virtually free group being finitely generated. If the endomorphism is uniformly continuous for the hyperbolic metric, it is proved that the set of regular fixed points in the hyperbolic boundary has finitely many orbits under the action of the finite fixed points. In the automorphism case, it is shown that these regular fixed points are either exponentially stable attractors or exponentially stable repellers.

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Efficient representatives for automorphisms of free products.

Cited by 29 publications

References 0 publications

Fixed subgroups in free groups: a survey

Fixed subgroups in free groups: a survey

Automorphisms of Hyperbolic Groups and Graphs of Groups

Fixed points of endomorphisms of virtually free groups

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