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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";
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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.
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A pair of handles with index differing by 1, whose cores link each other in a sufficiently simple way can be cancelled without changing the underlying manifold. Similarly, such a cancelling pair can be
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Two different smooth handlebody decompositions of a smooth 4-manifold are related by a finite sequence of
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There are also various tricks to modify surgery diagrams. One such useful move is the
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Describes how distinct surgery presentations of a given 3-manifold are related
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a pair of 3-balls (the attaching region of the 1-handle) or, more commonly,
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of the attaching maps, and the creation/cancellation of handle pairs.
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3-manifold is obtained by such surgery on some link in the 3-sphere.
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exhibited an equivalent construction in terms of a single move, the
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An extended set of diagrams and moves are used for describing
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are related by a sequence of Kirby moves. According to the
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A closed, smooth 4-manifold is usually described by a
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255:(1978). "A calculus for framed links in S".
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415:: CS1 maint: archived copy as title (
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43:using a finite set of moves, the
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352:Graduate Studies in Mathematics
178:A 2-handle is attached along a
348:4-Manifolds and Kirby Calculus
308:"On Kirby's calculus of links"
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327:10.1016/0040-9383(79)90010-7
143:unknotted circles with dots.
75:respectively, then they are
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346:; Stipsicz, András (1999).
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47:. Using four-dimensional
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51:, he proved that if
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265:(1): 35–56.
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65:Dehn surgery
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37:framed links
33:Robion Kirby
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320:(1): 1–15.
188:knot theory
180:solid torus
134:4-manifolds
61:3-manifolds
49:Cerf theory
45:Kirby moves
21:mathematics
402:2012-01-02
246:References
184:3-manifold
96:orientable
295:120770295
200:isotopies
127:slam-dunk
114:'s book,
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313:Topology
306:(1979).
206:See also
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