Regina Calculation Engine
Static Public Member Functions | List of all members
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 Linkunknot ()
 Returns a zero-crossing diagram of the unknot. More...
 
static Linkmonster ()
 Returns the monster unknot, a 10-crossing diagram of the unknot that is difficult to untangle. More...
 
static Linkgordian ()
 Returns Haken's Gordian unknot, a 141-crossing diagram of the unknot that is difficult to untangle. More...
 
static LinktrefoilLeft ()
 Returns a three-crossing diagram of the left-hand trefoil. More...
 
static LinktrefoilRight ()
 Returns a three-crossing diagram of the right-hand trefoil. More...
 
static Linktrefoil ()
 Returns a three-crossing diagram of the right-hand trefoil. More...
 
static LinkfigureEight ()
 Returns a four-crossing diagram of the figure eight knot. More...
 
static Linkhopf ()
 Returns a two-crossing diagram of the Hopf link. More...
 
static Linkwhitehead ()
 Returns a five-crossing diagram of the Whitehead link. More...
 
static Linkborromean ()
 Returns a six-crossing diagram of the Borromean rings. More...
 
static Linkconway ()
 Returns the 11-crossing Conway knot. More...
 
static LinkkinoshitaTerasaka ()
 Returns the 11-crossing Kinoshita-Terasaka knot. More...
 
static Linktorus (int p, int q)
 Returns the (p,q) torus link. More...
 
static Linkgst ()
 Returns a 48-crossing potential counterexample to the slice-ribbon conjecture, as described by Gompf, Scharlemann and Thompson. More...
 

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.

All of the methods in this class will assign an appropriate packet label to the link that they return.

Note that each of these routines constructs a new link from scratch. It is up to the caller of each routine to destroy the link that is returned.

Member Function Documentation

◆ borromean()

static Link* regina::ExampleLink::borromean ( )
static

Returns a six-crossing diagram of the Borromean rings.

Returns
a newly constructed link, which must be destroyed by the caller of this routine.

◆ 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
a newly constructed link, which must be destroyed by the caller of this routine.

◆ figureEight()

static Link* regina::ExampleLink::figureEight ( )
static

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

Returns
a newly constructed link, which must be destroyed by the caller of this routine.

◆ 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
a newly constructed link, which must be destroyed by the caller of this routine.

◆ 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", arXiv:1103.1601.

Returns
a newly constructed link, which must be destroyed by the caller of this routine.

◆ 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
a newly constructed link, which must be destroyed by the caller of this routine.

◆ 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
a newly constructed link, which must be destroyed by the caller of this routine.

◆ monster()

static Link* regina::ExampleLink::monster ( )
static

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

Returns
a newly constructed link, which must be destroyed by the caller of this routine.

◆ 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
pthe first parameter of the torus link; this must be strictly non-negative.
qthe 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
a newly constructed link, which must be destroyed by the caller of this routine.

◆ trefoilLeft()

static Link* regina::ExampleLink::trefoilLeft ( )
static

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

Returns
a newly constructed link, which must be destroyed by the caller of this routine.

◆ 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
a newly constructed link, which must be destroyed by the caller of this routine.

◆ unknot()

static Link* regina::ExampleLink::unknot ( )
static

Returns a zero-crossing diagram of the unknot.

Returns
a newly constructed link, which must be destroyed by the caller of this routine.

◆ whitehead()

static Link* regina::ExampleLink::whitehead ( )
static

Returns a five-crossing diagram of the Whitehead link.

Returns
a newly constructed link, which must be destroyed by the caller of this routine.

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

Copyright © 1999-2021, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).