Jerry L . Bon a
Nicolai Reshetikhi n
Leonard L . Scot t (Chair )
Partially supporte d b y th e NS F gran t DMS-962643 0
and J . S . Guggenhei m Memoria l Foundation ;
partially supporte d b y th e NS F gran t DMS-9022140.
1991 Mathematics Subject Classification. Primar y 53C15, 57N10;
Secondary 58F05 , 57R30 .
ABSTRACT. Th e theor y o f contac t structure s an d th e theor y o f foliation s hav e develope d rathe r
independently. The y com e fro m separat e traditions , an d hav e differen t flavors . However , i n
dimension 3 , the y hav e evolve d i n paralle l direction s tha t hav e powerfu l topologica l application s
involving tight contact structures o n th e on e han d an d taut foliations o n th e other .
The presen t wor k develop s th e foundation s fo r a theor y o f confoliations t o lin k thes e tw o the -
ories, wit h th e ai m o f developin g a combine d toolki t tha t include s bot h th e strongl y geometri c
constructions characteristi c o f foliatio n theor y an d th e analyti c tools , th e connection s t o four -
dimensional topology , an d th e flexibilit y characteristi c o f th e theor y o f contac t structures .
In particular , w e prove tha t ever y C
tau t foliatio n ca n b e C°-perturbe d t o giv e a tigh t contac t
Library o f Congres s Cataloging-in-Publicatio n Dat a
Eliashberg, Y. , 1946-
Confoliations / Yako v M . Eliashberg , Willia m P . Thurston .
p. cm . (Universit y lectur e series , ISS N 1047-3998 ; v. 13)
Includes bibliographica l references .
ISBN 0-8218-0776-5
1. Foliation s (Mathematics ) 2 . Three-manifold s (Topology ) I . Thurston , Willia m P. ,
1946- . II . Title . III . Series : Universit y lectur e serie s (Providence , R . I. ) ; 13.
QA613.62.E45 1997
514'.72—dc21 97-32128
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