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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Morse and generic contact between foliations


Author: Russell B. Walker
Journal: Trans. Amer. Math. Soc. 254 (1979), 265-281
MSC: Primary 58F15; Secondary 57R30, 58F18
MathSciNet review: 539918
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Abstract: Motivated by the recent work of J. Franks and C. Robinson, the study of the contact between two foliations of equal codimension is begun. Two foliations generically contact each other in certain dimensional sub-manifold complexes. All but a finite number of these contact points are ``Morse". In a recent paper by the author, a complete large isotopy ``index of contact'' is specified for two foliations of $ {T^2}$. If contact is restricted to index 0 ("domed contact"), some sharp conclusions are made as to the topology of the manifold and isotopy classes of the two foliations. It is hoped that this work will lead to the construction of new quasi-Anosov diffeomorphisms and possibly to a new Anosov diffeomorphism.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0539918-1
PII: S 0002-9947(1979)0539918-1
Article copyright: © Copyright 1979 American Mathematical Society