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Pontrjagin forms of quaternion manifolds.

Vasile Oproiu (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dimostra che per le varietà a struttura quaternionale generalizzata integrabile, le classi di Pontrjagin sono generate dalle classi di Pontrjagin del fibrato vettoriale fondamentale.

Positivity of Schur function expansions of Thom polynomials

Piotr Pragacz, Andrzej Weber (2007)

Fundamenta Mathematicae

Combining the approach to Thom polynomials via classifying spaces of singularities with the Fulton-Lazarsfeld theory of cone classes and positive polynomials for ample vector bundles, we show that the coefficients of the Schur function expansions of the Thom polynomials of stable singularities are nonnegative with positive sum.

Positivity of Thom polynomials II: the Lagrange singularities

Małgorzata Mikosz, Piotr Pragacz, Andrzej Weber (2009)

Fundamenta Mathematicae

We study Thom polynomials associated with Lagrange singularities. We expand them in the basis of Q̃-functions. This basis plays a key role in the Schubert calculus of isotropic Grassmannians. We prove that the Q̃-function expansions of the Thom polynomials of Lagrange singularities always have nonnegative coefficients. This is an analog of a result on the Thom polynomials of mapping singularities and Schur S-functions, established formerly by the last two authors.

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