Geodesic
Combinatorial mapping-torus, branched surfaces and free group automorphisms
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 3, pp. 405-440

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We give a characterization of the geometric automorphisms in a certain class of (not necessarily irreducible) free group automorphisms. When the automorphism is geometric, then it is induced by a pseudo-Anosov homeomorphism without interior singularities. An outer free group automorphism is given by a 1-cocycle of a 2-complex (a standard dynamical branched surface, see [7] and [9]) the fundamental group of which is the mapping-torus group of the automorphism. A combinatorial construction elucidates the link between this new representation (first introduced in [16]) and the classical representation of a free group automorphism by a graph-map [2].

Classification : 20E05, 57M20, 37Bxx, 37E25 
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     author = {Gautero, Fran\c{c}ois},
     title = {Combinatorial mapping-torus, branched surfaces and free group automorphisms},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {405--440},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 6},
     number = {3},
     year = {2007},
     mrnumber = {2370267},
     zbl = {1173.20017},
     language = {en},
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Gautero, François. Combinatorial mapping-torus, branched surfaces and free group automorphisms. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 6 (2007) no. 3, pp. 405-440. http://geodesic.mathdoc.fr/item/ASNSP_2007_5_6_3_405_0/