Homotopic Properties of the Spaces of Smooth Functions on a 2-Torus
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 _1O(f)=_1D _id (T^2)× _0S^′ (f)Z ^2× _0S^′ (f). The obtained result is true for a larger class of functions whose critical points are equivalent to homogeneous polynomials without multiple factors., number=9, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Maksimenko, S. I. and Feshchenko, B. G., year=2014, month=Sep., pages=1205–1212