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.

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
@article{ASNSP_2007_5_6_3_405_0,
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},
zbl = {1173.20017},
mrnumber = {2370267},
language = {en},
url = {http://archive.numdam.org/item/ASNSP_2007_5_6_3_405_0/}
}
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://archive.numdam.org/item/ASNSP_2007_5_6_3_405_0/

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