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Foliated cobordism classes of certain foliated $$S^ 1$$-bundles over surfaces. (English) Zbl 0555.57011
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, 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.
Reviewer: S.Goodman

##### MSC:
 57R30 Foliations in differential topology; geometric theory 57R32 Classifying spaces for foliations; Gelfand-Fuks cohomology 57R90 Other types of cobordism
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