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Classification and rigidity of totally periodic pseudo-Anosov flows in graph manifolds

Published online by Cambridge University Press:  03 July 2014

THIERRY BARBOT  and
SÉRGIO R. FENLEY
THIERRY BARBOT
Affiliation:
Université d’Avignon et des pays de Vaucluse, LANLG, Faculté des Sciences, 33 rue Louis Pasteur, 84000 Avignon, France email [email protected]
SÉRGIO R. FENLEY
Affiliation:
Florida State University, Tallahassee, FL 32306-4510, USA Princeton University, Princeton, NJ 08544-1000, USA email [email protected]
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Abstract

In this article we analyze totally periodic pseudo-Anosov flows in graph 3-manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a finite power of the free homotopy class of a closed orbit of the flow. We show that each such flow is topologically equivalent to one of the model pseudo-Anosov flows which we previously constructed in Barbot and Fenley (Pseudo-Anosov flows in toroidal manifolds. Geom. Topol. 17 (2013), 1877–1954). A model pseudo-Anosov flow is obtained by glueing standard neighborhoods of Birkhoff annuli and perhaps doing Dehn surgery on certain orbits. We also show that two model flows on the same graph manifold are isotopically equivalent (i.e. there is a isotopy of $M$ mapping the oriented orbits of the first flow to the oriented orbits of the second flow) if and only if they have the same topological and dynamical data in the collection of standard neighborhoods of the Birkhoff annuli.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 6 , September 2015 , pp. 1681 - 1722
Copyright
© Cambridge University Press, 2014 

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