2019
Том 71
№ 11

# Sharko V. V.

Articles: 19
Article (English)

### Functions and Vector Fields on $C(ℂP^N)$-Singular Manifolds

Ukr. Mat. Zh. - 2014. - 66, № 3. - pp. 311–315

Let $M^{2n+1}$ be a $C(ℂP^N)$ -singular manifold. We study functions and vector fields with isolated singularities on $M^{2n+1}$. A $C(ℂP^N)$ -singular manifold is obtained from a smooth manifold $M^{2n+1}$ with boundary in the form of a disjoint union of complex projective spaces $ℂP^n ∪ ℂP^n ∪ . . . ∪ ℂP^n$ with subsequent capture of a cone over each component of the boundary. Let $M^{2n+1}$ be a compact $C(ℂP^N)$ -singular manifold with k singular points. The Euler characteristic of $M^{2n+1}$ is equal to $X\left({M}^{2n+1}\right)=\frac{k\left(1-n\right)}{2}$. Let $M^{2n+1}$ be a $C(ℂP^n)$-singular manifold with singular points $m_1 , ... ,m_k$. Suppose that, on $M^{2n+1}$, there exists an almost smooth vector field $V(x)$ with finite number of zeros $m_1 , ... ,m_k , x_1 , ... ,x_l$. Then $X(M 2n + 1) = ∑_{i = 1}^l ind(x_i ) + ∑_{i = 1}^k ind(m_i )$.

Anniversaries (Ukrainian)

### Yurii Stephanovych Samoilenko (on his 70th birthday)

Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1408-1409

Anniversaries (Ukrainian)

### Anatolii Mykhailovych Samoilenko (on his 75th birthday)

Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 3 - 6

Article (English)

### $S^1$-bott functions on manifolds

Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1685-1698

We study $S^1$$-Bott functions on compact smooth manifolds. In particular, we investigate$S_1\$-invariant Bott functions on manifolds with circle action.

Anniversaries (Ukrainian)

### Oleksandr Ivanovych Stepanets’ (on the 70 th anniversary of his birthday)

Ukr. Mat. Zh. - 2012. - 64, № 5. - pp. 579-581

Anniversaries (Ukrainian)

### Yurii Ivanovych Samoilenko (on the 80th anniversary of his birthday)

Ukr. Mat. Zh. - 2012. - 64, № 4. - pp. 574-576

Article (English)

### Morse Functions on Cobordisms

Ukr. Mat. Zh. - 2011. - 63, № 1. - pp. 119-129

We study the homotopy invariants of crossed and Hilbert complexes. These invariants are applied to the calculation of exact values of Morse numbers of smooth cobordisms.

Anniversaries (Ukrainian)

### Yuri Yurievich Trokhimchuk (on his 80th birthday)

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 701 – 703

Anniversaries (Ukrainian)

### Fifty years devoted to science (on the 70th birthday of Anatolii Mykhailovych Samoilenko)

Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 3–7

Article (English)

### L2 -invariants and Morse - Smale flows on manifolds

Ukr. Mat. Zh. - 2007. - 59, № 4. - pp. 522-533

We study the homotopy invariants of free cochain and Hilbert complexes. These L2 -invariants are applied to the calculations of exact values of minimal numbers of closed orbits of some indexes of nonsingular Morse - Smale flows on manifolds of large dimensions.

Anniversaries (Ukrainian)

### Evgen Yakovich Khruslov (on his 75 th birthday)

Ukr. Mat. Zh. - 2007. - 59, № 4. - pp. 549-550

Anniversaries (Ukrainian)

### On the 90th birthday of Yurii Alekseevich Mitropol’skii

Ukr. Mat. Zh. - 2007. - 59, № 2. - pp. 147–151

Obituaries (Ukrainian)

### Andrei Reuter (1937-2006)

Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1584-1585

Article (Russian)

### Additive Functions and Chain Complexes of Projective Modules

Ukr. Mat. Zh. - 2004. - 56, № 2. - pp. 239-246

We study additive functions given on a category of finitely generated projective modules. Using these functions, we define p-minimal epimorphisms and give a necessary and sufficient condition for their existence. We prove results concerning the structure of p-minimal chains of projective modules.

Article (Russian)

### Smooth and Topological Equivalence of Functions on Surfaces

Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 687-700

We obtain conditions under which the Morse functions defined on surfaces are smooth equivalent and functions with isolated critical (singular) points are topologically equivalent.

Brief Communications (Russian)

### Topological aspects of dynamical systems on manifolds

Ukr. Mat. Zh. - 1993. - 45, № 6. - pp. 876–878

Necessary and sufficient conditions are presented for the existence of dynamical systems on manifolds, for which the set of nonwandering points consists of a disconnected union of 2-dimensional tori with a hyperbolic structure.

Article (Ukrainian)

### Exact round morse functions, Morse-type inequalities and integrals of Hamiltonian systems

Ukr. Mat. Zh. - 1989. - 41, № 6. - pp. 723–732

Article (Ukrainian)

### Morse numbers and minimal morse functions on nonsimply connected manifolds

Ukr. Mat. Zh. - 1988. - 40, № 1. - pp. 130–131

Article (Ukrainian)

### Stable algebra and Morse theory

Ukr. Mat. Zh. - 1980. - 32, № 5. - pp. 711–713