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A Giambelli-type formula for subbundles of the tangent bundle
Stockholm University, Faculty of Science, Department of Mathematics.
Independent University of Moscow.
2007 (English)In: Pacific Journal of Mathematics, ISSN 0030-8730, Pacific J. Math., Vol. 230, no 1, 233-255 p.Article in journal (Refereed) Published
Abstract [en]

Consider a generic n-dimensional subbundle V of the tangent bundle TM on some given manifold M. Given V one can define different degeneracy loci r(V), r = (r1 r2 r3 · · ·  rk) on M consisting of all points x 2 M for which the dimension of the subspace Vj (x)  TM(x) spanned by all length  j commutators of vector fields tangent to V at x is less than or equal to rj . Under a certain transversality assumption we ’explicitly’ calculate the Z2-cohomology classes of M dual to r(V) using determinantal formulas due to W. Fulton and the expression for the Chern classes of the associated bundle of the free Lie algebras in terms of the Chern classes of V.  

Place, publisher, year, edition, pages
2007. Vol. 230, no 1, 233-255 p.
Keyword [en]
n-subbundles; free Lie algebra; determinantal formulas
National Category
URN: urn:nbn:se:su:diva-20600ISI: 000251563400011OAI: diva2:187126
Available from: 2010-12-31 Created: 2007-11-28 Last updated: 2011-06-20Bibliographically approved

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