A codimension one flow is a transformation group (X,R(n-1),pi) where X is a compact n-dimensional topological manifold without boundary, R(n-1) is real Euclidean space of dimensions n-1, and pi is a flow map. It is known that if x is any point in x with discrete isotropy group, then x is contained in a transversal set (a section of the flow. It is shown that these sections can be chosen to be homeomorphic to the unit interval. Furthermore, if X contains a transversal set C which is homeomorphic to the unit circle, S(1), such that C times R(n-1) is a regular covering space of X (with covering projection pi), then pi sub 1(X) is a free Abelian group on finitely many generators whenever (x,R(n-1),pi) is minimal and isotropy free.
- Pub Date:
- February 1976
- Manifolds (Mathematics);
- One Dimensional Flow;
- Transformations (Mathematics);
- Euclidean Geometry;
- Fluid Mechanics and Heat Transfer