regina::ExampleLink Class Reference

This class offers routines for constructing ready-made examples of knots and links. More...

#include <link/examplelink.h>

Static Public Member Functions
static Link	unknot ()
	Returns a zero-crossing diagram of the unknot.
static Link	monster ()
	Returns the monster unknot, a 10-crossing diagram of the unknot that is difficult to untangle.
static Link	gordian ()
	Returns Haken's Gordian unknot, a 141-crossing diagram of the unknot that is difficult to untangle.
static Link	trefoilLeft ()
	Returns a three-crossing diagram of the left-hand trefoil.
static Link	trefoilRight ()
	Returns a three-crossing diagram of the right-hand trefoil.
static Link	trefoil ()
	Returns a three-crossing diagram of the right-hand trefoil.
static Link	figureEight ()
	Returns a four-crossing diagram of the figure eight knot.
static Link	hopf ()
	Returns a two-crossing diagram of the Hopf link.
static Link	whitehead ()
	Returns a five-crossing diagram of the Whitehead link.
static Link	borromean ()
	Returns a six-crossing diagram of the Borromean rings.
static Link	conway ()
	Returns the 11-crossing Conway knot.
static Link	kinoshitaTerasaka ()
	Returns the 11-crossing Kinoshita-Terasaka knot.
static Link	torus (int p, int q)
	Returns the (p,q) torus link.
static Link	gst ()
	Returns a 48-crossing potential counterexample to the slice-ribbon conjecture, as described by Gompf, Scharlemann and Thompson.

Detailed Description

This class offers routines for constructing ready-made examples of knots and links.

These examples may be useful for testing new code, or for simply getting a feel for how Regina works.

The sample links offered here may prove especially useful in Regina's scripting interface, where working with pre-existing files is more complicated than in the GUI.

Member Function Documentation

borromean()

static Link regina::ExampleLink::borromean ( )

static

Returns a six-crossing diagram of the Borromean rings.

Returns

the Borromean rings.

conway()

static Link regina::ExampleLink::conway ( )

static

Returns the 11-crossing Conway knot.

This is the reflection of K11n34 in the Knot Atlas, and is a mutant of the Kinoshita-Terasaka knot.

Returns

the Conway knot.

figureEight()

static Link regina::ExampleLink::figureEight ( )

static

Returns a four-crossing diagram of the figure eight knot.

Returns

the figure eight knot.

gordian()

static Link regina::ExampleLink::gordian ( )

static

Returns Haken's Gordian unknot, a 141-crossing diagram of the unknot that is difficult to untangle.

Returns

the Gordian unknot.

gst()

static Link regina::ExampleLink::gst ( )

static

Returns a 48-crossing potential counterexample to the slice-ribbon conjecture, as described by Gompf, Scharlemann and Thompson.

Specifically, this knot is Figure 2 from their paper "Fibered knots and potential counterexamples to the property 2R and slice-ribbon conjectures", Geometry & Topology 14 (2010), 2305-2347.

Returns

the Gompf-Scharlemann-Thompson knot.

hopf()

static Link regina::ExampleLink::hopf ( )

static

Returns a two-crossing diagram of the Hopf link.

This is the variant in which both crossings are positive.

Returns

the Hopf link.

kinoshitaTerasaka()

static Link regina::ExampleLink::kinoshitaTerasaka ( )

static

Returns the 11-crossing Kinoshita-Terasaka knot.

This is the reflection of K11n42 in the Knot Atlas, and is a mutant of the Conway knot. It has trivial Alexander polynomial.

Returns

the kinoshita-Terasaka knot.

monster()

static Link regina::ExampleLink::monster ( )

static

Returns the monster unknot, a 10-crossing diagram of the unknot that is difficult to untangle.

Returns

the monster unknot.

torus()

static Link regina::ExampleLink::torus ( int p, int q )

static

Returns the (p,q) torus link.

The parameters p and q must be non-negative, but they do not need to be coprime.

All of the crossings in the resulting link will be positive.

Parameters

p	the first parameter of the torus link; this must be strictly non-negative.
q	the second parameter of the torus link; this must also be strictly non-negative.

Returns

the (p, q) torus link.

trefoil()

static Link regina::ExampleLink::trefoil ( )

static

Returns a three-crossing diagram of the right-hand trefoil.

This returns the same knot as trefoilRight().

Returns

the right-hand trefoil.

trefoilLeft()

static Link regina::ExampleLink::trefoilLeft ( )

static

Returns a three-crossing diagram of the left-hand trefoil.

Returns

the left-hand trefoil.

trefoilRight()

static Link regina::ExampleLink::trefoilRight ( )

static

Returns a three-crossing diagram of the right-hand trefoil.

This returns the same knot as trefoil().

Returns

the right-hand trefoil.

unknot()

static Link regina::ExampleLink::unknot ( )

static

Returns a zero-crossing diagram of the unknot.

Returns

the unknot.

whitehead()

static Link regina::ExampleLink::whitehead ( )

static

Returns a five-crossing diagram of the Whitehead link.

Returns

the Whitehead link.

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The documentation for this class was generated from the following file:

• link/examplelink.h