Smooth maps having only singularities with Boardman symbol (1,0)

Cobordisms of maps with singularities of given class

“…These theorem show the importance of the homotopy type of Ω I (n, p). In [6], [7], [8] and [9] we have determined the homotopy type of Ω (i,0) (n, p) for i = max{n − p + 1, 1}, and studied NCob (Ω (i,0) n ,Ω (i,0) n+1 ) n,P and OCob…”

“…Th results of the paper show the importance of the homotopy type of Ω(n, p). In [1], [2], [4] and [5] we have described the homotopy type of Ω i,0 (n, p) for i = max{n − p + 1, 1} in terms of orthogonal groups and Stiefel manifolds. Although available only in the case of fold-maps, we will construct a simpler spectrum in Section 10 whose stable homotopy group is a direct summand of O(n, P ; Ω i,0 , Ω i,0 ) (respectively N(n, P ; Ω i,0 , Ω i,0 )) and also construct the corresponding classifying space.…”

Isotopy of Morin singularities

“…As an application, we consider in section 5 A-isotopy classes of n-Morin singularities appearing on stable perturbations of simple map-germs (R n , 0) → (R n , 0). We remark that homotopy types of the A 2 -orbit of the fold are considered by Ando [2,3], thus we are mainly interested in the case k ≥ 2. We also remark that this type of problem is asked by Nishimura [24].…”