Singular foliations of b^{k+1}-type are equivalent to k-th order foliations and are classified up to isotopy by fundamental group representations into the jet group G_{k,l}, with extension obstructed by a characteristic class.
The holonomy groupoid of a singular foliation
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$b^k$-algebroids and the variety of foliation jets
Singular foliations of b^{k+1}-type are equivalent to k-th order foliations and are classified up to isotopy by fundamental group representations into the jet group G_{k,l}, with extension obstructed by a characteristic class.