ISSN 2079-6900 (Print) 
ISSN 2587-7496 (Online)

Middle Volga Mathematical Society Journal

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MSC2010 37E30

Orientability of invariant foliations of pseudo-Anosovian homeomorphisms and branched coverings

A. Yu. Zhirov1

AnnotationIn this paper we give a description of a construction by means of a pseudo-Anosov homeomorphism (possibly generalized) of closed orientable surface whose invariant foliations are non-orientable, a two-sheeted covering (in general, branched) of this surface and a pseudo-Anosov homeomorphism of the covering surface that covers the original and has orientable invariant foliations are constructed. If the original homeomorphism does not have singularities of odd valency, then the covering that is constructed 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, and in the second the number of singularities of even valencies doubles and the features of doubled odd valences are added to them.
Keywordspseudo-Anosov homeomorphism, foliation with singularities, branched covering

1Alexey Yu. Zhirov, Professor, Moscow Aviation Institute (National Research University)   (125993, Russia, Moscow, Volokolamskoe Shosse, 4.), Dr. Sci. (Physics and Mathematics), ORCID:,

Citation: A. Yu. Zhirov, "[Orientability of invariant foliations of pseudo-Anosovian homeomorphisms and branched coverings]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:1 (2017) 30–37 (In Russian)

DOI 10.15507/2079-6900.19.2017.01.30-37