ON SPHERES IMBEDDED IN COMPACT DIFFERENTIABLE MANIFOLDS

Differentiable Actions on 2 « - Spheres

Introduction. It is shown in [4] that there is an infinite family of semifree Zm actions on odd dimensional homotopy spheres. There is also an infinite family of semifree S actions on odd dimensional homotopy spheres (see [2], [5]). On the other hand, it is announced in [2] that there are only finitely many inequivalent semifree S actions on even dimensional homotopy spheres. Hence it is intere...

Notes on Differentiable Manifolds

Lecture Notes on Differentiable Manifolds

1. Tangent Spaces, Vector Fields in R and the Inverse Mapping Theorem 1 1.1. Tangent Space to a Level Surface 1 1.2. Tangent Space and Vectors Fields on R 2 1.3. Operator Representations of Vector Fields 3 1.4. Integral Curves 4 1.5. Implicitand Inverse-Mapping Theorems 5 2. Topological and Differentiable Manifolds 9 3. Diffeomorphisms, Immersions, Submersions and Submanifolds 9 4. Fibre Bundle...

Differentiable Z9 Actions on Homotopy Spheres

The results of [4] proved that many exotic spheres do not admit smooth actions of relatively high-dimensional compact Lie groups (all group actions considered in this paper are assumed to be effective). It was clear that stronger results should hold in certain cases, and this was confirmed in [5]. A notable feature of [5] is the use of nonexistence theorems for certain smooth circle actions to ...

Differentiable piecewise-Bézier interpolation on Riemannian manifolds

We propose a generalization of classical Euclidean piecewiseBézier surfaces to manifolds, and we use this generalization to compute a C1-surface interpolating a given set of manifold-valued data points associated to a regular 2D grid. We then propose an efficient algorithm to compute the control points defining the surface based on the Euclidean concept of natural C2-splines and show examples o...