# Matings and the other side of the dictionary

Annales de la faculté des sciences de Toulouse Mathématiques (2012)

- Volume: 21, Issue: S5, page 1139-1147
- ISSN: 0240-2963

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topHubbard, John. "Matings and the other side of the dictionary." Annales de la faculté des sciences de Toulouse Mathématiques 21.S5 (2012): 1139-1147. <http://eudml.org/doc/250999>.

@article{Hubbard2012,

abstract = {In the theory of rational maps an important role is played by matings. These are probably the best understood of all rational functions, but they are bizarre, and involve gluing dendrites together to get spheres carrying Peano curves. In the theory of Kleinian groups, there is a parallel construction, the construction of double limits, that is central to Thurston’s hyperbolization theorem for 3-manifolds that fiber over the circle with pseudo-Anosov monodromy. It also involves gluing dendrites and Peano curves. Clearly these two constructions form one entry of the Sullivan dictionary. This article attempts to spell out the similarities and differences.},

author = {Hubbard, John},

journal = {Annales de la faculté des sciences de Toulouse Mathématiques},

keywords = {rational maps; polynomials; mating; manifold; foliation; Kleinian groups},

language = {eng},

month = {12},

number = {S5},

pages = {1139-1147},

publisher = {Université Paul Sabatier, Toulouse},

title = {Matings and the other side of the dictionary},

url = {http://eudml.org/doc/250999},

volume = {21},

year = {2012},

}

TY - JOUR

AU - Hubbard, John

TI - Matings and the other side of the dictionary

JO - Annales de la faculté des sciences de Toulouse Mathématiques

DA - 2012/12//

PB - Université Paul Sabatier, Toulouse

VL - 21

IS - S5

SP - 1139

EP - 1147

AB - In the theory of rational maps an important role is played by matings. These are probably the best understood of all rational functions, but they are bizarre, and involve gluing dendrites together to get spheres carrying Peano curves. In the theory of Kleinian groups, there is a parallel construction, the construction of double limits, that is central to Thurston’s hyperbolization theorem for 3-manifolds that fiber over the circle with pseudo-Anosov monodromy. It also involves gluing dendrites and Peano curves. Clearly these two constructions form one entry of the Sullivan dictionary. This article attempts to spell out the similarities and differences.

LA - eng

KW - rational maps; polynomials; mating; manifold; foliation; Kleinian groups

UR - http://eudml.org/doc/250999

ER -

## References

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