mathematical field of geometric topology, a handlebody is a decomposition of a manifold into standard pieces. Handlebodies play an important role in Morse theory...
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Genus (mathematics) (section Handlebody)
gluing the unit disk along the boundary. The genus of a 3-dimensional handlebody is an integer representing the maximum number of cuttings along embedded...
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Handle decomposition (redirect from Handlebody decomposition)
two types (i.e.: 0-handles and j-handles for some fixed j) is called a handlebody. When forming M union a j-handle H j {\displaystyle H^{j}} M ∪ f H j =...
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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...
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oriented 3-manifold that results from dividing it into two handlebodies. Let V and W be handlebodies of genus g, and let ƒ be an orientation reversing homeomorphism...
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orientable surface is null-cobordant, because it is the boundary of a handlebody. On the other hand, the 2n-dimensional real projective space P 2 n ( R...
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fiber space Heegaard splitting Waldhausen conjecture Compression body Handlebody Incompressible surface Dehn's lemma Loop theorem (aka the Disk theorem)...
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{\displaystyle S^{3}} is a handlebody. (The complement of a Seifert surface generated by the Seifert algorithm is always a handlebody.) For any knot the inequality...
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cut or boundary. This is closely related to, but not identical with, handlebody decompositions. More technically, the idea is to start with a well-understood...
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subset of a genus g handlebody in S³ (whose complement is also a genus g handlebody). If a link is a subset of a genus two handlebody, it is a double torus...
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boundary with that link Trigenus Compact, closed 3-manifolds Surgeries Three orientable handlebodies Unions along subsurfaces on boundaries of handlebodies...
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geometric topology, most commonly studied are Morse functions, which yield handlebody decompositions, while in mathematical analysis, one often studies solution...
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1960s by Stephen Smale, for differentiable manifolds. The development of handlebody theory allowed much the same proofs in the differentiable and PL categories...
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manifold of dimension not equal to 4 has a handlebody decomposition. Manifolds of dimension 4 have a handlebody decomposition if and only if they are smoothable...
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Andrews–Curtis conjecture. Andrews, J. J.; Curtis, M. L. (1965), "Free groups and handlebodies", Proceedings of the American Mathematical Society, 16 (2), American...
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Similarly, such a cancelling pair can be created. Two different smooth handlebody decompositions of a smooth 4-manifold are related by a finite sequence...
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cut or boundary. This is closely related to, but not identical with, handlebody decompositions. It is a major tool in the study and classification of...
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manifold of dimension not equal to 4 has a handlebody decomposition. Manifolds of dimension 4 have a handlebody decomposition if and only if they are smoothable...
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tunnels) that must be added to the knot so that the complement becomes a handlebody. The tunnel number can equally be defined for links. The boundary of a...
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Berkeley as a student of Robion Kirby. In topology, he has worked on handlebody theory, low-dimensional manifolds, symplectic topology, G2 manifolds....
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March 11, 2011. Andrews, J. J.; Curtis, M. L. (1965), "Free groups and handlebodies", Proceedings of the American Mathematical Society, 16 (2): 192–195,...
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mirror orbifold with underlying space a ball. It is double covered by a handlebody; the corresponding index 2 subgroup is a Kleinian group called a Schottky...
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defined by the conditions: K lies on a genus two Heegaard surface S in each handlebody bound by S, K meets some meridian disc exactly once. John Berge constructed...
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International Journal of Mathematics vol. 1, no 1 (1990) 29–46. Robert Gompf, Handlebody construction of Stein surfaces, Annals of Mathematics 148, (1998) 619–693...
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method used to decompose into handlebodies is the Heegaard splitting, which gives a decomposition in two handlebodies of equal genus. As an example:...
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a compact oriented 3-manifold that results from dividing it into two handlebodies. Every closed, orientable three-manifold may be so obtained; this follows...
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need not be complex, Annals of Mathematics, Volume 138, 1993, p. 61–111 Handlebody construction of Stein surfaces, Annals of Mathematics, Volume 148, 1998...
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topologically equivalent (homeomorphic) to a sphere, torus, or more general handlebody, classified by its number of handles. A non-orientable surface must be...
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is called an integral surgery. Such surgeries are closely related to handlebodies, cobordism and Morse functions. If all surgery coefficients are infinite...
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geometric topology, most commonly studied are Morse functions, which yield handlebody decompositions, which generalize to Morse–Bott functions and can be used...
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