Geodesic
Orientability of invariant foliations of pseudo-Anosovian homeomorphisms and branched coverings
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 1, pp. 30-37.

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper deals with pseudo-Anosov homeomorphism (possibly generalized) of closed orientable surface; invariant foliations of this mapping are supposed to be non-orientable. A construction is described that helps to build two-sheeted (in general, branched) covering of this surface and pseudo-Anosov homeomorphism of the covering surface that covers the original and has orientable invariant foliations. The covering and the homeomorphism are constructed by means of original mapping. If the original homeomorphism does not have singularities of odd valency then the constructed covering is not branched. Otherwise it has branch points of multiplicity 2 in singularities of odd valency. It is established that in the first case the covering homeomorphism has twice the number of singularities of the same valences as compared with the original. In the second case the number of singularities of even valencies doubles and the features of doubled odd valences are added to them.
Keywords: pseudo-Anosov homeomorphisms, foliations with singularities, branched coverings. 
@article{SVMO_2017_19_1_a2,
     author = {A. Yu. Zhirov},
     title = {Orientability of invariant foliations of {pseudo-Anosovian} homeomorphisms and branched coverings},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {30--37},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2017_19_1_a2/}
}
TY  - JOUR
AU  - A. Yu. Zhirov
TI  - Orientability of invariant foliations of pseudo-Anosovian homeomorphisms and branched coverings
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2017
SP  - 30
EP  - 37
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2017_19_1_a2/
LA  - ru
ID  - SVMO_2017_19_1_a2
ER  - 
%0 Journal Article
%A A. Yu. Zhirov
%T Orientability of invariant foliations of pseudo-Anosovian homeomorphisms and branched coverings
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2017
%P 30-37
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2017_19_1_a2/
%G ru
%F SVMO_2017_19_1_a2
A. Yu. Zhirov. Orientability of invariant foliations of pseudo-Anosovian homeomorphisms and branched coverings. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 19 (2017) no. 1, pp. 30-37. http://geodesic.mathdoc.fr/item/SVMO_2017_19_1_a2/

[1] A. Fathi, F. Laudenbach, V. Poenaru, Travaux de Thurston sur les surfaces. Orsay seminaire, Asterisque, 66–67, 1979 | MR

[2] E. Casson, S. Bleiler, Automorphisms of Surfaces after Nielsen and Thurston, London Mathematical Society Student Texts, Cambridge University Press, Cambridge, 1988 (In Russ.)

[3] R.V. Plykin, “Sources and sinks of A-diffeomorphisms of surfaces”, Matem. sbornik, 94:2 (1974), 243–264 (In Russ) | MR

[4] H. Masur, J. Smille, “Quadratic differentials with prescribed singularities and pseudo-Anosov diffeomorphisms”, Comment. Math. Helvetici, 68 (1993), 289–307 | DOI | MR | Zbl

[5] A.U. Zhirov, Topological conjugency of pseudo-Anosov homeomorphismes, MCCNE, M., 2013 (In Russ)

[6] A.B. Katok, B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995 (In Eng.) | MR