Homotopic Properties of the Spaces of Smooth Functions on a 2-Torus
Abstract
Let f : T 2 → ℝ be a Morse function on a 2-torus, let S(f) and O (f) be, respectively, its stabilizer and orbit with respect to the right action of the group D (T 2) of diffeomorphisms of T 2, let D id(T 2), be the identity path component of the group D (T 2), and let S′(f) = S(f) ∩ D id(T 2). We present sufficient conditions under which \uppi1O(f)=\uppi1Did(T2)×\uppi0S′(f)≡Z2×\uppi0S′(f). The obtained result is true for a larger class of functions whose critical points are equivalent to homogeneous polynomials without multiple factors.Downloads
Published
25.09.2014
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Section
Research articles
How to Cite
Maksimenko, S. I., and B. G. Feshchenko. “Homotopic Properties of the Spaces of Smooth Functions on a 2-Torus”. Ukrains’kyi Matematychnyi Zhurnal, vol. 66, no. 9, Sept. 2014, pp. 1205–1212, https://umj.imath.kiev.ua/index.php/umj/article/view/2211.