Title: Orientability of Manifolds. The Fundamental Group. Covering Spaces (Fibre Bundles with Discrete Fibre)
Abstract: According to the simplest of the definitions of an orientation on a manifold given above (see Definition 1.1.3), a manifold M is oriented if the local coordinate systems x α j given on the members U j of a covering collection of local co-ordinate neighbourhoods (or charts) for M, are such that the transition functions from one local co-ordinate system to another on the regions of overlap U j ∩ U k , have positive Jacobian: $$\det \left( {\frac{{\partial x_j^\alpha }}{{\partial x_k^\beta }}} \right) > 0.$$
Publication Year: 1985
Publication Date: 1985-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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