 
Summary: Pergamon Topology Vol. 36, No I, pp. 209227, 1997
Copyright 0 1996 Elsevier Science Ltd
Printed in Great Britain. All rtghts reserved
WO9383/96/%15.tXl+ 0.00
00409383(95)000666
FINITE FOLIATIONS AND SIMILARITY
MAPS
INTERVAL EXCHANGE
D. COOPER+,D. D. LONG*
and A. W. RE~D$
(Received 10 February 1995; receioedfor publication 30 November 1995)
1. INTRODUCTION
This paper continues the study, initiated in [l], of understanding surfaces immersed
transverse to the suspension flow in a hyperbolic surface bundle over the circle. Briefly, our
context is the following. Suppose that 8 :F + F is an orientationpreserving pseudoAnosov
homeomorphism of a closed surface. Then we may form the mapping torus M = M(0)
which results of Thurston show is hyperbolic. This mapping torus is equipped with an
obvious onedimensional foliation, denoted throughout as 9. We shall consider surfaces
g :.%+A4which are immersed into M so as to be transverse to 9. It is shown by Mangum in
[2] that such surfaces are automatically incompressible. It follows that g.+(rci(S)) is
