The Godbillon-Vey invariant of a transversely homogeneous foliation

Brooks, Robert; Goldman, William

doi:10.1090/S0002-9947-1984-0760978-9

The Godbillon-Vey invariant of a transversely homogeneous foliation
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Trans. Amer. Math. Soc. 286 (1984), 651-664 Request permission

Abstract:

A real projective foliation is a foliation $\mathfrak {F}$ with a system of local coordinates transverse to $\mathfrak {F}$ modelled on ${\mathbf {R}}{P^1}$ (so that the coordinate changes are real linear fractional transformations). Given a closed manifold $M$, there is but a finite set of values in ${H^3}(M;{\mathbf {R}})$ which the Godbillon-Vey invariant of such foliations may assume. A bound on the possible values, in terms of the fundamental group, is computed. For $M$ an oriented circle bundle over a surface, this finite set is explicitly computed.

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