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\begin{document}

\title{Quasigeodesic Flows in Hyperbolic $3$-manifolds}
\author{S\'{e}rgio Fenley and Lee Mosher
\thanks{Research at MSRI is supported in part by NSF graph DMS-9022140.
Both authors were supported by additional NSF grants.}
}
%Mathematical Sciences Research Institute}
\maketitle

\bigskip

\begin{abstract}
Any closed, oriented,  hyperbolic
$3$-manifold with nontrivial second homology has many quasigeodesic
flows, where quasigeodesic means that flow lines are uniformly efficient
in measuring  distance in relative homotopy classes. The flows are
pseudo-Anosov flows which are  almost transverse to finite depth
foliations in the manifold. The main tool is the use of a sutured
manifold hierarchy which has good geometric properties.
\end{abstract}

\bigskip


\input{qflintro.tex}

\input{qfl1.tex}

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\input{qfl4.tex}

\input{bib.tex}

\vskip .6in
\noindent
University of California, Berkeley and

\noindent
Mathematical Sciences Research Institute 

\noindent
(Fenley)

\vskip .3in
\noindent
Mathematical Sciences Research Institute 

\noindent
(Mosher)



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