Foliated cobordism classes of certain foliated \(S^ 1\)-bundles over surfaces
For foliated circle bundles over oriented surfaces with a particular structure group, it is shown that the Godbillon-Vey invariant is a complete invariant for \(C^{\infty}\)-foliated cobordism classes. In particular, \textit{W. Thurston}'s examples [Bull. Am. Math. Soc. 78, 511- 514 (1972; Zbl 0266.57004)] are cobordant to zero if their Godbillon-Vey invariants are zero.
foliated circle bundles over oriented surfaces
scientific article; zbMATH DE number 3884995