A. O. Prishlyak

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Articles: 5

Maps of 2-manifolds into the plane

A. M. Bondarenko, A. O. Prishlyak

↓ Abstract   |   Article (.pdf)

MFAT 18 (2012), no. 3, 220-229


We define a $p$-graph and describe how it changes under isotopy of projections for classification of maps of $2$-manifolds into plane. The problem of graph implementation and maps classification are considered.

Morse functions and flows on nonorientable surfaces

D. P. Lychak, A. O. Prishlyak

↓ Abstract   |   Article (.pdf)

MFAT 15 (2009), no. 3, 251-258


The present paper deals with the correspondence between Morse functions and flows on nonorientable surfaces. It is proved that for every Morse flow with an indexing of saddle points on a nonorientable surface there is a unique Morse function, up to a fiber equivalence, such that its gradient flow is trajectory equivalent to the initial flow, and the values of the function in the saddle points are ordered according to the indexing. The algorithm for constructing the Morse function from a Morse flow with an indexing is given. Reeb graphs and 3-graphs, which assign Morse functions and the corresponding Morse flows with the number of the saddle points less than $3$ are presented.

Classification of noncompact surfaces with boundary

A. O. Prishlyak, K. I. Mischenko

↓ Abstract   |   Article (.pdf)

MFAT 13 (2007), no. 1, 62–66


We give a topological classification of noncompact surfaces with any number of boundary components.

Morse functions with finite number of singularities on a plane

A. O. Prishlyak

MFAT 8 (2002), no. 1, 75-78


On topologically equivalent Morse functions on 3-manifold

A. O. Prishlyak

MFAT 5 (1999), no. 3, 49-53


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