Topology of the spaces of functions with prescribed singularities on surfaces (Q334402)

The author studies the space of smooth functions with prescribed local singularities of the \(A_{\mu}\)-type on a smooth \(2\)-dimensional surface. The homotopy type of this space, endowed with the \(C^{\infty}\)-topology, and its decomposition into orbits is described. Other authors paper directly connected to this interesting topic are [Mosc. Univ. Math. Bull. 67, No. 4, 151--157 (2012; Zbl 1282.58011); translation from Vestn. Mosk. Univ., Ser. I 67, No. 4, 14--20 (2012); Sb. Math. 204, No. 1, 75--113 (2013; Zbl 1277.58007); translation from Mat. Sb. 204, No. 1, 79--118 (2013); Math. Notes 92, No. 2, 219--236 (2012; Zbl 1261.55002); translation from Mat. Zametki 92, No. 2, 241--261 (2012); Sb. Math. 190, No. 3, 349--405 (1999; Zbl 0941.57026); translation from Mat. Sb. 190, No. 3, 29--88 (1999)].