Cusp cobordism group of Morse functions

By a Morse function on compact manifold with boundary we mean real-valued without critical points near the such that its as well of restriction to are all nondegenerate. For functions, Saeki and Yamamoto have previously defined certain notion cusp cobordism, computed unoriented cobordism group functions surfaces. In this paper, compute oriented groups manifolds any dimension by employing Levine’s elimination technique complementary process creating pairs cusps along fold lines. We show both cyclic order two in even dimensions, infinite odd dimensions. surfaces our result yields an explicit description Saeki–Yamamoto’s invariant which they constructed means cohomology universal complex singular fibers.