A giambelli-type formula for subbundles of the tangent bundle

Boris Shapiro, Maxim Kazarian

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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 Σr (V), r=(r1 ≤ r2 ≤ r3 ≤· · ·≤ rk), on M consisting of all points x ε M for which the subspaces Vj (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 Z2- cohomology classes of M dual to Σr (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 languageEnglish
Pages (from-to)233-255
Number of pages23
JournalPacific Journal of Mathematics
Volume230
Issue number1
DOIs
Publication statusPublished - 2007
Externally publishedYes

Keywords

  • Determinantal formulas
  • Free Lie algebra
  • n-subbundles

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