Cone-Decompositions and Degenerate Critical Points
Octavian Cornea · Proceedings of the London Mathematical Society · 1998
Let M be a compact, smooth, 2-connected, 2m-dimensional manifold with ∂M simply connected. If M has the homotopytype of an m-dimensional CW-complex, then it supports a smooth, self-indexed function, maximal, constant and regular on ∂M with at most cat(M) + 2 critical points, all of which are of a certain ‘reasonable’ type. To such a critical point there corresponds, homotopically, the attachment of a cone. Conversely, to a cone attachment we may associate, under certain dimensionality and connectivity conditions, a ‘reasonable’ critical point. 1991 Mathematics Subject Classification: primary 55M30, 57R70; secondary 58E05, 55P50, 55P62.