Abstract
is a vector space isomorphism of Vn onto T(m). The tangent bundle 3(M) of the manifold M consists of the ordered pairs (m, v) where meM and vE T(m). Therefore, as a point set only, 3(M) is M x V1. We shall assume that the reader is familiar with the fibre space topology which is customarily assigned to 3(M). (For a description of this topology and the facts concerning fibre bundles which we shall need in other parts of this paper see N. Steenrod, The topology of fibre bundles, Princeton, 1951.) For many manifolds M this topology differs from the topology of the product space M X Vn. This fact indicates that it is the assignment of this topology which makes 3(M) an interesting mathematical object. It is the purpose of this paper to present an intrinsic characterization of this topology.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.