论文信息 - On the Structure of Manifolds

On the Structure of Manifolds

In this paper, we prove a number of theorems which give some insight into the structure of differentiable manifolds. The methods, results and some notation of [13], hereafter referred to as GPC, and [12] will be used. These two papers and [14] can be considered as a starting point for this one. The main theorems in these papers are special cases of the theorems here. Among the most important theorems in this paper are 1. 1 and 6. 1. Some conversations with A. Haefliger were helpful in the preparation of parts of this paper. Everything will be considered from the differentable, equivalently C*, point of view; manifolds, imbeddings, and isotopes will be C*.

S. Smale | Steve Smale

[1] Arnold Shapiro,et al. Obstructions to the Imbedding of a Complex in a Euclidean Space.: I. The First Obstruction , 1957 .

[2] S. Smale. On Gradient Dynamical Systems , 1961 .

[3] M. Hirsch. Immersions of manifolds , 1959 .

[4] A. Haefliger,et al. Knotted (4k - 1)-Spheres in 6k-Space , 1962 .

[5] H. Whitney. The Self-Intersections of a Smooth n-Manifold in 2n-Space , 1944 .

[6] J. Milnor. Differentiable manifolds which are homotopy spheres , 1959 .

[7] C. Wall. Classi?cation of (n ? 1)-connected 2n-manifolds , 1962 .

[8] Barry Mazur,et al. A Note on Some Contractible 4-Manifolds , 1961 .

[9] S. Smale. Generalized Poincare's Conjecture in Dimensions Greater Than Four , 1961 .