Knots and Links

Knots and links in the 3-sphere. More...

Classes
class	regina::ExampleLink
	This class offers routines for constructing ready-made examples of knots and links. More...
class	regina::StrandRef
	A reference to one of the two strands of a link that pass each other at a crossing. More...
class	regina::Crossing
	Represents a single crossing in a link diagram. More...
class	regina::Link
	Represents a directed knot or link in the 3-sphere. More...
class	regina::ModelLinkGraphArc
	A reference to an outgoing edge from a node of a model graph for a knot or link. More...
class	regina::ModelLinkGraphNode
	Represents a single node in a model graph for a knot or link. More...
class	regina::ModelLinkGraph
	Represents an undirected 4-valent planar graph with a specific planar embedding. More...
class	regina::ModelLinkGraphCells
	Describes the cellular decomposition of the sphere that is induced by a given planar 4-valent graph. More...
class	regina::Tangle
	Represents a 2-tangle in the 3-ball. More...

Enumerations
enum	regina::Framing { regina::FRAMING_SEIFERT = 1 , regina::FRAMING_BLACKBOARD = 2 }
	Indicates one of the standard framings of a knot or link. More...

Functions
std::ostream &	regina::operator<< (std::ostream &out, const StrandRef &s)
	Writes a depiction of the given strand reference to the given output stream. More...
void	regina::swap (Link &lhs, Link &rhs)
	Swaps the contents of the two given links. More...
std::ostream &	regina::operator<< (std::ostream &out, const ModelLinkGraphArc &a)
	Writes a depiction of the given arc reference to the given output stream. More...
void	regina::swap (ModelLinkGraph &lhs, ModelLinkGraph &rhs) noexcept
	Swaps the contents of the two given graphs. More...
void	regina::swap (Tangle &lhs, Tangle &rhs) noexcept
	Swaps the contents of the two given tangles. More...

Detailed Description

Knots and links in the 3-sphere.

Enumeration Type Documentation

Framing

enum regina::Framing

Indicates one of the standard framings of a knot or link.

Here a framing refers to a choice of normal vector field along the knot or link. Equivalently, a framing refers to a choice of longitude on the torus bounding each component of the link.

Enumerator
FRAMING_SEIFERT	Indicates the Seifert framing, which is defined algebraically and is independent of the knot/link projection. For each component of the link, draw a Seifert surface (i.e., an orientable surface embedded in the 3-sphere that is bounded by the corresponding knot). The Seifert framing is the vector field that points into the corresponding surface. Equivalently, for each component of the link, the Seifert framing chooses the unique longitude for the corresponding knot that is trivial in the homology of the knot complement.
FRAMING_BLACKBOARD	Indicates the blackboard framing, which is specific to the knot/link projection. For the blackboard framing, the normal vector field stays within the projection plane. Equivalently, the blackboard framing chooses longitudes whose projections do not intersect the original link diagram.

Function Documentation

operator<<() [1/2]

std::ostream & regina::operator<< ( std::ostream &  out, const ModelLinkGraphArc &  a  )

inline

Writes a depiction of the given arc reference to the given output stream.

Parameters

out	the output stream to which to write.
a	the arc reference to write.

Returns

a reference to the given output stream.

operator<<() [2/2]

std::ostream & regina::operator<< ( std::ostream &  out, const StrandRef &  s  )

inline

Writes a depiction of the given strand reference to the given output stream.

The reference will be written in the form ^n or _n, denoting the upper or lower strand at crossing n respectively. For example, the upper strand of crossing 7 will be written as ^7.

Parameters

out	the output stream to which to write.
s	the reference to write.

Returns

a reference to the given output stream.

swap() [1/3]

void regina::swap ( Link &  lhs, Link &  rhs  )

inline

Swaps the contents of the two given links.

This global routine simply calls Link::swap(); it is provided so that Link meets the C++ Swappable requirements.

See Link::swap() for more details.

Note

This swap function is not marked noexcept, since it fires change events on both links which may in turn call arbitrary code via any registered packet listeners.

Parameters

lhs	the link whose contents should be swapped with rhs.
rhs	the link whose contents should be swapped with lhs.

swap() [2/3]

void regina::swap ( ModelLinkGraph &  lhs, ModelLinkGraph &  rhs  )

inlinenoexcept

Swaps the contents of the two given graphs.

This global routine simply calls ModelLinkGraph::swap(); it is provided so that ModelLinkGraph meets the C++ Swappable requirements.

See ModelLinkGraph::swap() for more details.

Parameters

lhs	the graph whose contents should be swapped with rhs.
rhs	the graph whose contents should be swapped with lhs.

swap() [3/3]

void regina::swap ( Tangle &  lhs, Tangle &  rhs  )

inlinenoexcept

Swaps the contents of the two given tangles.

This global routine simply calls Tangle::swap(); it is provided so that Tangle meets the C++ Swappable requirements.

See Tangle::swap() for more details.

Parameters

lhs	the tangle whose contents should be swapped with rhs.
rhs	the tangle whose contents should be swapped with lhs.