The Space of (Contact) Anosov Flows on 3-Manifolds

J. Math. Sci. Univ. Tokyo
Vol. 20 (2013), No. 3, Page 445–460.

Matsumoto, Shigenori
The Space of (Contact) Anosov Flows on 3-Manifolds
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The first half of this paper concerns the topology of the space $\cal{A}$$(M)$ of (not necessarily contact) Anosov vector fields on the unit tangent bundle $M$ of closed oriented hyperbolic surfaces $\Sigma$. We show that there are countably infinite connected components of $\cal{A}$$(M)$, each of which is not simply connected. In the second part, we study contact Anosov flows. We show in particular that the time changes of contact Anosov flows form a $C^1$-open subset of the space of the Anosov flows which leave a particular $C^\infty$ volume form invariant, if the ambiant manifold is a rational homology sphere.

Keywords: Anosov flows, contact Anosov flows, $C^1$-open subset.

Mathematics Subject Classification (2010): Primary 37D20; Secondary 37C40.
Mathematical Reviews Number: MR3156989

Received: 2013-08-26