In recent year s th e stud y o f foliation s o n manifolds ha s become a n area o f intens e
research activity, an d substantial progres s ha s been made o n a variety o f interestin g
problems. I n particular, grea t stride s hav e been made toward understanding th e questio
of ho w many geometrically distinc t foliations , i f any , ca n be constructe d o n a given
manifold. Th e wor k on this specifi c proble m has mature d int o a beautiful theory , an d
the purpose o f thes e note s i s t o introduc e th e reader t o its mai n aspects .
The note s ar e based o n lectures give n i n a Regional Conferenc e a t Washington Un
versity i n January 1975. I want to expressm y gratitude t o Larry Conlon, Bil l Boothb y
and Gary Jensen, whos e har d work and constant suppor t mad e that conferenc e an d thes
notes possible . I also wan t to thank Jod y Anderson for her very capabl e assistanc e i n
preparing th e manuscript .
H. Blaine Lawson, jr.
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