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On Thom Polynomials for A4(−) via Schur Functions

Öztürk, Özer (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 05E05, 14N10, 57R45.We study the structure of the Thom polynomials for A4(−) singularities. We analyze the Schur function expansions of these polynomials. We show that partitions indexing the Schur function expansions of Thom polynomials for A4(−) singularities have at most four parts. We simplify the system of equations that determines these polynomials and give a recursive description of Thom polynomials for A4(−) singularities. We also give Thom polynomials...

On topological degree and Poincaré duality

Franco Cardin (1995)

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

In this Note we investigate about some relations between Poincaré dual and other topological objects, such as intersection index, topological degree, and Maslov index of Lagrangian submanifolds. A simple proof of the Poincaré-Hopf theorem is recalled. The Lagrangian submanifolds are the geometrical, multi-valued, solutions of physical problems of evolution governed by Hamilton-Jacobi equations: the computation of the algebraic number of the branches is showed to be performed by using Poincaré dual....

On topological invariants of vector bundles

Zbigniew Szafraniec (1992)

Annales Polonici Mathematici

Let E → W be an oriented vector bundle, and let X(E) denote the Euler number of E. The paper shows how to calculate X(E) in terms of equations which describe E and W.

On two results of Singhof

Augustin-Liviu Mare (1997)

Commentationes Mathematicae Universitatis Carolinae

For a compact connected semisimple Lie group G we shall prove two results (both related with Singhof’s paper [13]) on the Lusternik-Schnirelmann category of the adjoint orbits of G , respectively the 1-dimensional relative category of a maximal torus T in G . The techniques will be classical, but we shall also apply some basic results concerning the so-called 𝒜 -category (cf. [14]).

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