ON THE HOMOMORPHISM H* (B IRδ) → H* (BDiff∞C(IR)δ)

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This chapter focuses on the homomorphism H* (B IRδ)→H* (BDiff ∞c(IR)δ) and describes the cobordisms of foliations without holonomy. A foliated S1-bundle over Tn is foliated cobordant to zero if its total holonomies are contained in a one-parameter subgroup of Diff(S1) generated by a smooth vector field. The group homology is the homology of the classifying space for the group with the discrete topology.