TY - JOUR AU - S. I. Maksimenko AU - B. G. Feshchenko PY - 2014/09/25 Y2 - 2024/03/29 TI - Homotopic Properties of the Spaces of Smooth Functions on a 2-Torus JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 66 IS - 9 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2211 AB - 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 $$ {\uppi}_1\mathcal{O}(f)={\uppi}_1{\mathcal{D}}_{\mathrm{id}}\left({T}^2\right)\times {\uppi}_0S^{\prime }(f)\equiv {\mathrm{\mathbb{Z}}}^2\times {\uppi}_0S^{\prime }(f). $$ The obtained result is true for a larger class of functions whose critical points are equivalent to homogeneous polynomials without multiple factors. ER -