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CHARLES CONLE Y
writer learned a lot a t th e conferenc e an d has incorporated man y o f th e suggestion s an d
ideas o f th e othe r participant s into thes e notes . I n particular , thank s ar e owe d t o Joh n
Montgomery fo r discussion s o f th e presen t versio n o f th e continuatio n theorem s whic h ar e
properly credite d t o him. Richar d Churchill' s theore m (whic h predate s th e conference )
inspired th e ide a that somethin g aki n t o th e Mors e index wa s a central objec t o f study. Th e
theorem i s only briefl y discusse d becaus e mor e cohomolog y theor y i s necessary t o d o a
proper job. Tha t theore m i s also properly labeled .
The ideas o f Rober t Easto n pervad e al l th e work ; but i n th e presen t for m ther e i s no
single theorem t o whic h his name is attached. Thi s is an injustice whic h mus t occu r fre -
quently in a subject wherei n s o much wor k an d s o many ideas ar e summarized i n on e head-
line calle d a theorem. O n the othe r hand , many mathematician s ar e known chiefl y becaus e
their name i s attached t o a remark whic h wa s dropped in the cours e o f a difficult proo f an d
was useful enoug h t o b e picked u p an d elevate d t o th e statu s o f s o and so' s theore m (o r in-
equality). Easto n has at least avoide d tha t fat e u p t o now. I n an y case , he i s responsible
for man y o f th e thought s tha t ar e here.
Richard McGehee , Clark Robinson an d James Yorke have made som e very usefu l sug -
gestions, many o f whic h have been followed . An d t o Joh n Evans , Ed Fadell, Neil Fenichel ,
Paul Rabinowit z an d Joe l Smolle r th e write r owe s a great deb t fo r thei r encouragemen t a s
well as their willingnes s to share many o f thei r ideas an d much o f their time .
Also, the autho r mus t than k Henr y Kurlan d fo r pointin g ou t som e major mistake s an d
omissions. I n his thesis he has give n complete proof s o f severa l o f th e theorem s whos e
proofs wer e omitte d here.
Finally, the autho r i s most indebte d t o JtirgenMoser , no t onl y fo r som e direc t hel p
on thi s projec t but , primarily, fo r th e instruction , insight s an d advic e he has offere d ove r
several years.
Charles Conley, Madison, Wisconsin
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