## Abstract

Consider a generic n-dimensional subbundle V of the tangent bundle TM on some manifold M. Given V, one can define different degeneracy loci Σ_{r} (V), r=(r_{1} ≤ r_{2} ≤ r_{3} ≤· · ·≤ r_{k}), on M consisting of all points x ε M for which the subspaces V^{j} (x)⊂TM (x) spanned by all length ≤ j commutators of vector fields tangent to V at x has dimension less than or equal to rj . Under a certain transversality assumption, we explicitly calculate the Z_{2}- cohomology classes of M dual to Σ_{r} (V), using determinantal formulas due toW. Fulton and the expression of the Chern classes of the associated bundle of the free Lie algebras in terms of the Chern classes of V.

Original language | English |
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Pages (from-to) | 233-255 |

Number of pages | 23 |

Journal | Pacific Journal of Mathematics |

Volume | 230 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 |

Externally published | Yes |

## Keywords

- Determinantal formulas
- Free Lie algebra
- n-subbundles