Glossary of differential geometry and topology
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- Glossary of general topology
- Glossary of algebraic topology
- Glossary of Riemannian and metric geometry.
Words in italics denote a self-reference to this glossary.
Bundle, see fiber bundle.
Doubling, given a manifold M with boundary, doubling is taking two copies of M and identifying their boundaries. As the result we get a manifold without boundary.
Fiber. In a fiber bundle, π: E → B the preimage π−1(x) of a point x in the base B is called the fiber over x, often denoted Ex.
Hypersurface. A hypersurface is a submanifold of codimension one.
Manifold. A topological manifold is a locally Euclidean Hausdorff space. (In Wikipedia, a manifold need not be paracompact or second-countable.) A Ck manifold is a differentiable manifold whose chart overlap functions are k times continuously differentiable. A C∞ or smooth manifold is a differentiable manifold whose chart overlap functions are infinitely continuously differentiable.
Neat submanifold. A submanifold whose boundary equals its intersection with the boundary of the manifold into which it is embedded.
Surface, a two-dimensional manifold or submanifold.
Tangent bundle, the vector bundle of tangent spaces on a differentiable manifold.
Tangent field, a section of the tangent bundle. Also called a vector field.
Whitney sum. A Whitney sum is an analog of the direct product for vector bundles. Given two vector bundles α and β over the same base B their cartesian product is a vector bundle over B ×B. The diagonal map induces a vector bundle over B called the Whitney sum of these vector bundles and denoted by α⊕β.