Generic systems of co-rank one vector distributions
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- Trans. Amer. Math. Soc. 358 (2006), 4521-4531 Request permission
Abstract:
This paper studies a generic class of sub-bundles of the complexified tangent bundle. Involutive, generic structures always exist and have Levi forms with only simple zeroes. For a compact, orientable three-manifold the Chern class of the sub-bundle is mod $2$ equivalent to the Poincaré dual of the characteristic set of the associated system of linear partial differential equations.References
- Michael F. Atiyah, Vector fields on manifolds, Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen, Heft 200, Westdeutscher Verlag, Cologne, 1970 (English, with German and French summaries). MR 0263102, DOI 10.1007/978-3-322-98503-3
- Raoul Bott, Lectures on characteristic classes and foliations, Lectures on algebraic and differential topology (Second Latin American School in Math., Mexico City, 1971) Lecture Notes in Math., Vol. 279, Springer, Berlin, 1972, pp. 1–94. Notes by Lawrence Conlon, with two appendices by J. Stasheff. MR 0362335
- Howard Jacobowitz, Whitney and Mizohata structures, Geometric analysis of PDE and several complex variables, Contemp. Math., vol. 368, Amer. Math. Soc., Providence, RI, 2005, pp. 293–304. MR 2126476, DOI 10.1090/conm/368/06785
- Howard Jacobowitz, Maps into complex space, Proc. Amer. Math. Soc. 134 (2006), no. 3, 893–895. MR 2180907, DOI 10.1090/S0002-9939-05-08056-1
- Howard Jacobowitz and Gerardo Mendoza, Sub-bundles of the complexified tangent bundle, Trans. Amer. Math. Soc. 355 (2003), no. 10, 4201–4222. MR 1990583, DOI 10.1090/S0002-9947-03-03350-6
- Harold I. Levine, Elimination of cusps, Topology 3 (1965), no. suppl, suppl. 2, 263–296. MR 176484, DOI 10.1016/0040-9383(65)90078-9
- Emery Thomas, Fields of tangent $k$-planes on manifolds, Invent. Math. 3 (1967), 334–347. MR 217814, DOI 10.1007/BF01402957
- Emery Thomas, Fields of tangent $2$-planes on even-dimensional manifolds, Ann. of Math. (2) 86 (1967), 349–361. MR 212834, DOI 10.2307/1970692
- Hassler Whitney, On singularities of mappings of euclidean spaces. I. Mappings of the plane into the plane, Ann. of Math. (2) 62 (1955), 374–410. MR 73980, DOI 10.2307/1970070
Additional Information
- Howard Jacobowitz
- Affiliation: Department of Mathematics, Rutgers University, Camden, New Jersey 08102
- MR Author ID: 190037
- Email: jacobowi@camden.rutgers.edu
- Received by editor(s): September 8, 2004
- Published electronically: March 24, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 358 (2006), 4521-4531
- MSC (2000): Primary 58J10; Secondary 57R20
- DOI: https://doi.org/10.1090/S0002-9947-06-03998-5
- MathSciNet review: 2231386