- handlebody
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A top-dimensional submanifold of Euclidean space comprising a ball with handles attached to it along its boundary.
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handlebody
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Handlebody — In the mathematical field of geometric topology, a handlebody is a particular kind of manifold. Handlebodies are most often used to study 3 manifolds, although they can be defined in arbitrary dimensions. General definition Let G be a connected… … Wikipedia
Handle decomposition — In mathematics, a handle decomposition of an n manifold M is a representation of that manifold as an exhaustion:M 0 subset M 1 subset dots subset Mwhere each M i is obtained from M {i 1}by attaching a n i handle. Handle decompositions are never… … Wikipedia
Handle (mathematics) — In topology, a branch of mathematics, a handle is just a topological ball; it is called a handle because of the context in which it is discussed, of which there are two: handle decompositions and handlebodies.A handle is a subset of a manifold… … Wikipedia
Compression body — In the theory of 3 manifolds, a compression body is a kind of generalized handlebody. A compression body is either a handlebody or the result of the following construction: Let S be a compact, closed surface (not necessarily connected). Attach 1… … Wikipedia
Genus (mathematics) — In mathematics, genus has a few different, but closely related, meanings:TopologyOrientable surfaceThe genus of a connected, orientable surface is an integer representing the maximum number of cuttings along closed simple curves without rendering … Wikipedia
List of geometric topology topics — This is a list of geometric topology topics, by Wikipedia page. See also: topology glossary List of topology topics List of general topology topics List of algebraic topology topics Publications in topology Contents 1 Low dimensional topology 1.1 … Wikipedia
4-manifold — In mathematics, 4 manifold is a 4 dimensional topological manifold. A smooth 4 manifold is a 4 manifold with a smooth structure. In dimension four, in marked contrast with lower dimensions, topological and smooth manifolds are quite different.… … Wikipedia
Surgery theory — In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one manifold from another in a controlled way, introduced by Milnor (1961). Surgery refers to cutting out parts of the manifold… … Wikipedia
Double torus knot — A double torus knot is a closed curve drawn on the surface called a double torus (think of the surface of two doughnuts stuck together). More technically, a double torus knot is the homeomorphic image of a circle in S³ which can be realized as a… … Wikipedia
Anse (Mathématiques) — Pour les articles homonymes, voir anse. Dans le sous domaine des mathématiques de la topologie, une anse est une balle topologique. On les retrouve dans deux contextes. Une anse peut être un sous ensemble d une variété. C est un des éléments de… … Wikipédia en Français
