I. Kuznietsova

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20192023

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4 papers · 1 filter

math.GT2023

Geometric interpretation of First Betti numbers of smooth functions orbits

Iryna Kuznietsova, Yuliia Soroka

Let $M$ be a 2-disk or a cylinder, and $f$ be a smooth function on $M$ with constant values at $\partial M$ , devoid of critical points in $\partial M$ , and exhibiting a property wh…

math.GT2023

Deformational symmetries of smooth functions on non-orientable surfaces

Iryna Kuznietsova, Sergiy Maksymenko

Given a compact surface $M$ , consider the natural right action of the group of diffeomorphisms $D (M)$ of $M$ on $C^{\infty} (M, R)$ defined by the rule:…

math.GT2021

Reversing orientation homeomorphisms of surfaces

Iryna Kuznietsova, Sergiy Maksymenko

Let $M$ be a connected compact orientable surface, $f : M \to R$ be a Morse function, and $h : M \to M$ be a diffeomorphism which preserves $f$ in the sense that $f \circ h = f$ .…

math.GT2019

Homotopy properties of smooth functions on the Möbius band

Iryna Kuznietsova, Sergiy Maksymenko

Let $B$ be a Möbius band and $f : B \to R$ be a Morse map taking a constant value on $\partial B$ , and $S (f, \partial B)$ be the group of diffeomorphisms $h$ of $B$ …