ON SUITABLE MANIFOLDS,
Abstract
M is a manifold and G(M) denotes the group of all homeomorphisms of M onto itself with the compactopen topology. For a point e belonging to M, M is suitable if there exists a continuous map T: M approaching G(M) such that T (x)(x)=e and T (e) = identity. This note shows that when M is compact, suitability is equivalent to the existence on M of a continuous multiplication which has many of the properties of a group multiplication. A definition is also given of suitability for differentiable manifolds with a proof that such manifolds are parallelizable. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 30, 1963
- Accession Number
- AD0617856
Entities
People
- Robert F. Brown
Organizations
- University of California, Los Angeles