Measured foliations and handlebodies. (English) Zbl 0628.57010
The mapping class group acts on Thurston’s sphere of measured foliations [W. Thurston, The geometry and topology of 3-manifolds, unpublished Lect. Notes, Princeton)]. Here, the action of its subgroup consisting of homeomorphisms that extend to the handlebody is studied. Properties of the limit set and domain of discontinuity are described and for genus two it is shown that the limit set has measure zero.
Reviewer: S.V.Duzhin
MSC:
| 57N05 | Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010) |
| 57R30 | Foliations in differential topology; geometric theory |
| 57S30 | Discontinuous groups of transformations |
| 57R50 | Differential topological aspects of diffeomorphisms |
Keywords:
space of measured foliations on a 2-manifold; mapping class group; homeomorphisms that extend to the handlebody; limit set; domain of discontinuityReferences:
| [1] | Veech, J. D’ Analyse Math 33 pp 222– (1978) |
| [2] | Rees, Ergod. Th. & Dynam. Sys. 1 pp 461– (1981) |
| [3] | Kerckhoff, Ergod. Th. & Dynam. Sys. 5 pp 257– (1985) |
| [4] | DOI: 10.2307/2373474 · Zbl 0227.32007 · doi:10.2307/2373474 |
| [5] | DOI: 10.2307/1971341 · Zbl 0497.28012 · doi:10.2307/1971341 |
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