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Theoretical survey synthesizes integrability, cobordism, and classifying spaces in manifold topology, highlighting structural classification across dimensions.
Foliations of dimension-one. 3. Higher dimensional foliations; integrability criteria. 4. Foliations of codimension-one; existence theorems. 5. Notions of equivalence; foliated cobordism groups. 6. The general theory; classifying spaces and characteristic classes for foliations. 7. Results on open manifolds; the classification theory of Gromov-Haefliger-Phillips. 8. Results on closed manifolds; questions of compact leaves and stability.
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H. Blaine Lawson (1974) studied this question.
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