Let f : T 2 → ℝ be a Morse function on a 2-torus, let S(f) and \( \mathcal{O} \)(f) be, respectively, its stabilizer and orbit with respect to the right action of the group \( \mathcal{D} \)(T 2) of diffeomorphisms of T 2, let \( \mathcal{D} \) id(T 2), be the identity path component of the group \( \mathcal{D} \)(T 2), and let S′(f) = S(f) ∩ \( \mathcal{D} \) id(T 2). We present sufficient conditions under which
The obtained result is true for a larger class of functions whose critical points are equivalent to homogeneous polynomials without multiple factors.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 9, pp. 1205–1212, September, 2014.
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Maksymenko, S.I., Feshchenko, B.G. Homotopic Properties of the Spaces of Smooth Functions on a 2-Torus. Ukr Math J 66, 1346–1353 (2015). https://doi.org/10.1007/s11253-015-1014-3
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DOI: https://doi.org/10.1007/s11253-015-1014-3