NON-RIGIDITY OF CYCLIC AUTOMORPHIC ORBITS IN FREE GROUPS
نویسندگان
چکیده
منابع مشابه
Non-Rigidity of Cyclic automorphic orbits in Free Groups
We say a subset Σ ⊆ FN of the free group of rank N is spectrally rigid if whenever T1, T2 ∈ cvN are R-trees in (unprojectivized) outer space for which ‖σ‖T1 = ‖σ‖T2 for every σ ∈ Σ, then T1 = T2 in cvN . The general theory of (non-abelian) actions of groups on R-trees establishes that T ∈ cvN is uniquely determined by its translation length function ‖ · ‖T : FN → R, and consequently that FN its...
متن کاملSpectral rigidity of automorphic orbits in free groups
It is well-known that a point T 2 cvN in the (unprojectivized) Culler–Vogtmann Outer space cvN is uniquely determined by its translation length function k kT W FN !R . A subset S of a free group FN is called spectrally rigid if, whenever T;T 0 2 cvN are such that kgkT D kgkT 0 for every g 2 S then T D T 0 in cvN . By contrast to the similar questions for the Teichmüller space, it is known that ...
متن کاملCorrigendum: “Spectral rigidity of automorphic orbits in free groups”
Lemma 5.1 in our paper [5] says that every infinite normal subgroup of Out.FN / contains a fully irreducible element; this lemma was substantively used in the proof of the main result, Theorem A in [5]. Our proof of Lemma 5.1 in [5] relied on a subgroup classification result of Handel and Mosher [8], originally stated in [8] for arbitrary subgroups H Out.FN / . It subsequently turned out (see H...
متن کاملCorrigendum to “Spectral rigidity of automorphic orbits in free groups”
Lemma 5.1 in our paper [6] says that every infinite normal subgroup of Out(FN) contains a fully irreducible element; this lemma was substantively used in the proof of the main result, Theorem A in [6]. Our proof of Lemma 5.1 in [6] relied on a subgroup classification result of Handel-Mosher [9], originally stated in [9] for arbitrary subgroups H ≤ Out(FN). It subsequently turned out (see p. 1 i...
متن کاملAutomorphic orbits in free groups
Let Fn be the free group of a finite rank n. We study orbits Orbφ(u), where u is an element of the group Fn, under the action of an automorphism φ. If an orbit like that is finite, we determine precisely what its cardinality can be if u runs through the whole group Fn, and φ runs through the whole group Aut(Fn). Another problem that we address here is related to Whitehead’s algorithm that deter...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2012
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s021819671250021x