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1

On topological invariants of vector bundles

100%

Szafraniec Z.

Annales Polonici Mathematici

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1991-1992

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tom 56

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nr 3

295-301

EN

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.

2

An algebraic method for calculating the topological degree

63%

Łęcki A., Szafraniec Z.

Banach Center Publications

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1996

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tom 35

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nr 1

73-83

3

On the Euler characteristic of fibres of real polynomial maps

63%

Parusiński A., Szafraniec Z.

Banach Center Publications

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1998

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tom 44

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nr 1

175-182

EN

Let Y be a real algebraic subset of $𝑹^m$ and $F:Y → 𝑹^n$ be a polynomial map. We show that there exist real polynomial functions $g_1, ..., g_s$ on $𝑹^n$ such that the Euler characteristic of fibres of $F$ is the sum of signs of $g_i$.

4

On families of trajectories of an analytic gradient vector field

63%

Dzedzej A., Szafraniec Z.

Annales Polonici Mathematici

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2005

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tom 87

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nr 1

99-109

EN

For an analytic function f:ℝⁿ,0 → ℝ,0 having a critical point at the origin, we describe the topological properties of the partition of the family of trajectories of the gradient equation ẋ = ∇f(x) attracted by the origin, given by characteristic exponents and asymptotic critical values.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Banach Center Publications

4 Szafraniec Z.

1 Dzedzej A.

1 Parusiński A.

1 Łęcki A.

1 2005

1 1998

1 1996

1 1992

On topological invariants of vector bundles

An algebraic method for calculating the topological degree

On the Euler characteristic of fibres of real polynomial maps

On families of trajectories of an analytic gradient vector field