# Combinatorial mapping-torus, branched surfaces and free group automorphisms

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2007)

- Volume: 6, Issue: 3, page 405-440
- ISSN: 0391-173X

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topGautero, François. "Combinatorial mapping-torus, branched surfaces and free group automorphisms." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 6.3 (2007): 405-440. <http://eudml.org/doc/272278>.

@article{Gautero2007,

abstract = {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].},

author = {Gautero, François},

journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},

keywords = {geometric automorphisms; free group automorphisms; pseudo-Anosov homeomorphisms; outer automorphisms; dynamical branched surfaces; fundamental groups; mapping-torus groups},

language = {eng},

number = {3},

pages = {405-440},

publisher = {Scuola Normale Superiore, Pisa},

title = {Combinatorial mapping-torus, branched surfaces and free group automorphisms},

url = {http://eudml.org/doc/272278},

volume = {6},

year = {2007},

}

TY - JOUR

AU - Gautero, François

TI - Combinatorial mapping-torus, branched surfaces and free group automorphisms

JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

PY - 2007

PB - Scuola Normale Superiore, Pisa

VL - 6

IS - 3

SP - 405

EP - 440

AB - 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].

LA - eng

KW - geometric automorphisms; free group automorphisms; pseudo-Anosov homeomorphisms; outer automorphisms; dynamical branched surfaces; fundamental groups; mapping-torus groups

UR - http://eudml.org/doc/272278

ER -

## References

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