Handlebody information

mathematical field of geometric topology, a handlebody is a decomposition of a manifold into standard pieces. Handlebodies play an important role in Morse theory...

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 =...

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...

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...

fiber space Heegaard splitting Waldhausen conjecture Compression body Handlebody Incompressible surface Dehn's lemma Loop theorem (aka the Disk theorem)...

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...

Berkeley as a student of Robion Kirby. In topology, he has worked on handlebody theory, low-dimensional manifolds, symplectic topology, G2 manifolds....

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...

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...

geometric topology, most commonly studied are Morse functions, which yield handlebody decompositions, while in mathematical analysis, one often studies solution...

{\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...

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...

1960s by Stephen Smale, for differentiable manifolds. The development of handlebody theory allowed much the same proofs in the differentiable and PL categories...

Similarly, such a cancelling pair can be created. Two different smooth handlebody decompositions of a smooth 4-manifold are related by a finite sequence...

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...

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...

boundary with that link Trigenus Compact, closed 3-manifolds Surgeries Three orientable handlebodies Unions along subsurfaces on boundaries of handlebodies...

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...

need not be complex, Annals of Mathematics, Volume 138, 1993, p. 61–111 Handlebody construction of Stein surfaces, Annals of Mathematics, Volume 148, 1998...

the number of arcs that must be added to make the knot complement a handlebody Writhe Berge conjecture Birman–Wenzl algebra Clasper (mathematics) Eilenberg–Mazur...

Akbulut (2012) showed that the Dolgachev surface X 3 {\displaystyle X_{3}} has a handlebody decomposition without 1- and 3-handles. Akbulut, Selman (2012). "The Dolgachev...

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...

geometric topology, most commonly studied are Morse functions, which yield handlebody decompositions, which generalize to Morse–Bott functions and can be used...

n-manifolds ( n ≥ 4 {\displaystyle n\geq 4} ) presented as CW complexes or handlebodies, there is no algorithm for determining if they are isomorphic (homeomorphic...