Positivity of legendrian thom polynomials

Ma lgorzata Mikosz Warsaw University of Technology Piotr Praga Institute of Mathematics of Polish Academy of Sciences Andrzej Weber University of Warsaw

Differential Geometry mathscidoc:1609.10236

Journal of Differential Geometry, 89, (1), 111-132, 2011
We study Legendrian singularities arising in complex contact geometry. We define a one-parameter family of bases in the ring of Legendrian characteristic classes such that any Legendrian Thom polynomial has nonnegative coefficients when expanded in these bases. The method uses a suitable Lagrange Grassmann bundle on the product of projective spaces. This is an extension of a nonnegativity result for Lagrangian Thom polynomials obtained by the authors previously. For a fixed specialization, other special- izations of the parameter lead to upper bounds for the coefficients of the given basis. One gets also upper bounds of the coefficients from the positivity of classical Thom polynomials (of singularities of mappings), obtained previously by the last two authors.
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  author={Ma lgorzata Mikosz, Piotr Praga, and Andrzej Weber},
  booktitle={Journal of Differential Geometry},
Ma lgorzata Mikosz, Piotr Praga, and Andrzej Weber. POSITIVITY OF LEGENDRIAN THOM POLYNOMIALS. 2011. Vol. 89. In Journal of Differential Geometry. pp.111-132. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160913205859921145897.
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