It is well known ([2], [3], [5]) that
all the closed manifolds with zero Euler characteristic admit
foliations of codimension one. In [1] (see also
[4]), the notion of geometric entropy for foliations of
closed Riemannian manifolds has been introduced. From the definition
it follows easily that the conditions "zero entropy" or "positive
entropy" do not depend on Riemannian structures. So, without
referring to Riemannian structures, one has two types of foliations:
these with zero entropy and those with positive entropy.
In the talk, we will discuss the problem of existence of
codimension-one foliations of these two types.
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References- E. Ghys, R. Langevin, P. Walczak, Entropie
géométrique des feuilletages , Acta Math. 160, 1988,
105--142.
- W. Likorish, A foliation for 3-manifolds ,
Ann. of Math. 82, 1965, 414--420.
- W. Thurston, Existence of codimension-one
foliations , Ann. of Math. 104, 1976, 249--268.
- P. Walczak, Dynamics of Foliations, Groups
and Pseudogroups , Birkhäuser 2004.
- J. Wood, Foliations on 3-manifolds , Ann. of
Math. 89, 1969, 336--358.
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