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- Kirby_calculus abstract "In mathematics, the Kirby calculus in geometric topology, named after Robion Kirby, is a method for modifying framed links in the 3-sphere using a finite set of moves, the Kirby moves. Using four-dimensional Cerf theory, he proved that if M and N are 3-manifolds, resulting from Dehn surgery on framed links L and J respectively, then they are homeomorphic if and only if L and J are related by a sequence of Kirby moves. According to the Lickorish–Wallace theorem any closed orientable 3-manifold is obtained by such surgery on some link in the 3-sphere.Some ambiguity exists in the literature on the precise use of the term "Kirby moves". Different presentations of "Kirby calculus" have a different set of moves and these are sometimes called Kirby moves. Kirby's original formulation involved two kinds of move, the "blow-up" and the "handle slide"; Roger Fenn and Colin Rourke exhibited an equivalent construction in terms of a single move, the Fenn–Rourke move, that appears in many expositions and extensions of the Kirby calculus. Dale Rolfsen's book, Knots and Links, from which many topologists have learned the Kirby calculus, describes a set of two moves: 1) delete or add a component with surgery coefficient infinity 2) twist along an unknotted component and modify surgery coefficients appropriately (this is called the Rolfsen twist). This allows an extension of the Kirby calculus to rational surgeries.There are also various tricks to modify surgery diagrams. One such useful move is the slam-dunk.An extended set of diagrams and moves are used for describing 4-manifolds.A framed link in the 3-sphere encodes instructions for attaching 2-handles to the 4-ball.(The 3-dimensional boundary of this manifold is the 3-manifold interpretation of the link diagram mentioned above.) 1-handles are denoted by either (a) a pair of 3-balls (the attaching region of the 1-handle) or, more commonly, (b) unknotted circles with dots. The dot indicates that a neighborhood of a standard 2-disk with boundary the dotted circle is to be excised from the interior of the 4-ball. Excising this 2-handle is equivalent to adding a 1-handle. 3-handles and 4-handles are usually not indicated in the diagram.".
- Kirby_calculus wikiPageID "1105826".
- Kirby_calculus wikiPageLength "3856".
- Kirby_calculus wikiPageOutDegree "29".
- Kirby_calculus wikiPageRevisionID "682906588".
- Kirby_calculus wikiPageWikiLink 3-manifold.
- Kirby_calculus wikiPageWikiLink 3-sphere.
- Kirby_calculus wikiPageWikiLink 4-manifold.
- Kirby_calculus wikiPageWikiLink Adjunction_space.
- Kirby_calculus wikiPageWikiLink Attaching_map.
- Kirby_calculus wikiPageWikiLink Ball_(mathematics).
- Kirby_calculus wikiPageWikiLink C._P._Rourke.
- Kirby_calculus wikiPageWikiLink Category:Geometric_topology.
- Kirby_calculus wikiPageWikiLink Cerf_theory.
- Kirby_calculus wikiPageWikiLink Closure_(mathematics).
- Kirby_calculus wikiPageWikiLink Colin_P._Rourke.
- Kirby_calculus wikiPageWikiLink Dale_Rolfsen.
- Kirby_calculus wikiPageWikiLink Dehn_surgery.
- Kirby_calculus wikiPageWikiLink Exotic_R4.
- Kirby_calculus wikiPageWikiLink Fenn–Rourke_move.
- Kirby_calculus wikiPageWikiLink Framed_link.
- Kirby_calculus wikiPageWikiLink Geometric_topology.
- Kirby_calculus wikiPageWikiLink Graduate_Studies_in_Mathematics.
- Kirby_calculus wikiPageWikiLink Handle_decomposition.
- Kirby_calculus wikiPageWikiLink Homeomorphic.
- Kirby_calculus wikiPageWikiLink Homeomorphism.
- Kirby_calculus wikiPageWikiLink Homotopy.
- Kirby_calculus wikiPageWikiLink Knot_(mathematics).
- Kirby_calculus wikiPageWikiLink Knot_theory.
- Kirby_calculus wikiPageWikiLink Lickorish–Wallace_theorem.
- Kirby_calculus wikiPageWikiLink Mathematics.
- Kirby_calculus wikiPageWikiLink Orientability.
- Kirby_calculus wikiPageWikiLink Orientable.
- Kirby_calculus wikiPageWikiLink Robert_Gompf.
- Kirby_calculus wikiPageWikiLink Robion_Kirby.
- Kirby_calculus wikiPageWikiLink Rolfsen_twist.
- Kirby_calculus wikiPageWikiLink Slam-dunk.
- Kirby_calculus wikiPageWikiLink Solid_torus.
- Kirby_calculus wikiPageWikiLinkText "Kirby calculus".
- Kirby_calculus hasPhotoCollection Kirby_calculus.
- Kirby_calculus subject Category:Geometric_topology.
- Kirby_calculus hypernym Method.
- Kirby_calculus type Software.
- Kirby_calculus comment "In mathematics, the Kirby calculus in geometric topology, named after Robion Kirby, is a method for modifying framed links in the 3-sphere using a finite set of moves, the Kirby moves. Using four-dimensional Cerf theory, he proved that if M and N are 3-manifolds, resulting from Dehn surgery on framed links L and J respectively, then they are homeomorphic if and only if L and J are related by a sequence of Kirby moves.".
- Kirby_calculus label "Kirby calculus".
- Kirby_calculus sameAs カービー計算.
- Kirby_calculus sameAs m.046g5p.
- Kirby_calculus sameAs Q5956316.
- Kirby_calculus sameAs Q5956316.
- Kirby_calculus sameAs 卡比微積分.
- Kirby_calculus wasDerivedFrom Kirby_calculus?oldid=682906588.
- Kirby_calculus isPrimaryTopicOf Kirby_calculus.