Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Stability of foliations


Authors: Harold I. Levine and Michael Shub
Journal: Trans. Amer. Math. Soc. 184 (1973), 419-437
MSC: Primary 58A30; Secondary 57D30
MathSciNet review: 0331417
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let X be a compact manifold and let k be an integer. It is shown that the set of homeomorphism conjugacy classes of germs at X of foliations of codimension k and the set of homeomorphism conjugacy classes of (holonomy) representations of $ {\prod _1}(X)$ in the group of germs at 0 of 0-fixed self-diffeomorphisms of $ {{\text{R}}^k}$ are homeomorphic when given appropriate topologies. Stable foliation germs and stable holonomy representations correspond under this homeomorphism. It is shown that there are no stable foliation germs at a toral leaf if the dimension of the torus is greater than one.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 58A30, 57D30

Retrieve articles in all journals with MSC: 58A30, 57D30


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0331417-X
PII: S 0002-9947(1973)0331417-X
Article copyright: © Copyright 1973 American Mathematical Society