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Measured foliations and handlebodies

Published online by Cambridge University Press:  19 September 2008

Howard Masur
Howard Masur
Affiliation:
Department of Mathematics, University of Illinois, Chicago, IL 60680, USA
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Abstract

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We consider the action of the subgroup of the mapping class group consisting of homeomorphisms that extend to the handlebody on Thurston's sphere of measured foliations. Properties of the limit set and domain of discontinuity are described and for genus two it is shown the limit set has measure zero.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 1 , March 1986 , pp. 99 - 116
Copyright
Copyright © Cambridge University Press 1986

References

REFERENCES

[1]Fathi, A., Laudenbach, F., Poenaru, V. et al. . Travaux.de Thurston sur les surfaces, Asterisque, pp. 66–67 (1979).Google Scholar
[2]Floyd, W.. Hyperbolic manifolds, 3 manifold constructions, and actions of subgroups of Mod (g) on PL(Sg). To appear.Google Scholar
[3]Harer, J. & Penner, R.. Combinatorics of train tracks. To appear.Google Scholar
[4]Kerckhoff, S.. Simplicial systems for interval exchange maps and measured foliations. Ergod. Th. & Dynam. Sys. 5 (1985), 257–271.CrossRefGoogle Scholar
[5]Maskit, B.. Self-maps of Kleinian groups. Amer. J. Math 93 (1971), 840–856.CrossRefGoogle Scholar
[6]Masur, H.. Interval exchange transformations and measured foliations. Annals of Math. 115 (1982), 169–200.CrossRefGoogle Scholar
[7]Rees, M.. An alternative approach to the ergodic theory of measured foliations on surfaces. Ergod. Th. & Dynam. Sys. 1 (1981), 461–485.CrossRefGoogle Scholar
[8]Thurston, W.. On the dynamics of diffeomorphisms of surfaces. Preprint.Google Scholar
[9]Thurston, W.. The geometry and topology of 3-manifolds. Lecture Notes, Princeton.Google Scholar
[10]Veech, W.. Interval exchange transformations. J. D' Analyse Math 33 (1978), 222–278.CrossRefGoogle Scholar