Standard 3-Manifolds

Standard 3-manifolds whose structures are well-understood. More...

Classes
class	regina::NGraphLoop
	Represents a closed graph manifold formed by joining a single bounded Seifert fibred space to itself along a torus. More...
class	regina::NGraphPair
	Represents a closed graph manifold formed by joining two bounded Seifert fibred spaces along a common torus. More...
class	regina::NGraphTriple
	Represents a closed graph manifold formed by joining three bounded Seifert fibred spaces along their torus boundaries. More...
class	regina::NHandlebody
	Represents an arbitrary handlebody. More...
class	regina::NLensSpace
	Represents a general lens space. More...
class	regina::NManifold
	Represents a particular 3-manifold. More...
struct	regina::NSFSFibre
	Represents an exceptional (alpha, beta) fibre in a Seifert fibred space. More...
class	regina::NSFSpace
	Represents a general Seifert fibred space, which may be orientable or non-orientable. More...
class	regina::NSFSAltSet
	Provides a variety of alternative representations of a single bounded Seifert fibred space. More...
class	regina::NSimpleSurfaceBundle
	Represents a particularly simple closed surface bundle over the circle. More...
class	regina::NSnapPeaCensusManifold
	Represents a 3-manifold from the SnapPea cusped census. More...
class	regina::NTorusBundle
	Represents a torus bundle over the circle. More...

Enumerations
enum	regina::NSFSpace::classType {   regina::NSFSpace::o1 = 101, regina::NSFSpace::o2 = 102, regina::NSFSpace::n1 = 201, regina::NSFSpace::n2 = 202,   regina::NSFSpace::n3 = 203, regina::NSFSpace::n4 = 204, regina::NSFSpace::bo1 = 301, regina::NSFSpace::bo2 = 302,   regina::NSFSpace::bn1 = 401, regina::NSFSpace::bn2 = 402, regina::NSFSpace::bn3 = 403 }
	Lists the six classes o1, o2, n1, n2, n3, n4 for base orbifolds without boundaries, plus five classes bo1, b02, bn1, bn2, bn3 for base orbifolds with boundaries. More...

Functions
REGINA_API std::ostream &	regina::operator<< (std::ostream &out, const NSFSFibre &f)
	Writes the given fibre in human-readable format to the given output stream. More...

Detailed Description

Standard 3-manifolds whose structures are well-understood.

Enumeration Type Documentation

enum regina::NSFSpace::classType

Lists the six classes o1, o2, n1, n2, n3, n4 for base orbifolds without boundaries, plus five classes bo1, b02, bn1, bn2, bn3 for base orbifolds with boundaries.

Enumerator
o1	Indicates that the base orbifold is orientable with no punctures or reflector boundaries, and that none of its generators give fibre-reversing paths.
o2	Indicates that the base orbifold is orientable with no punctures or reflector boundaries, and that all of its generators give fibre-reversing paths.
n1	Indicates that the base orbifold is non-orientable with no punctures or reflector boundaries, and that none of its generators give fibre-reversing paths.
n2	Indicates that the base orbifold is non-orientable with no punctures or reflector boundaries, and that all of its generators give fibre-reversing paths.
n3	Indicates that the base orbifold is non-orientable with no punctures or reflector boundaries, that it has non-orientable genus at least two, and that precisely one of its generators gives a fibre-reversing path.
n4	Indicates that the base orbifold is non-orientable with no punctures or reflector boundaries, that it has non-orientable genus at least three, and that precisely two of its generators give fibre-reversing paths.
bo1	Indicates that the base orbifold contains punctures and/or reflector boundaries, that it is orientable, and that it contains no fibre-reversing paths.
bo2	Indicates that the base orbifold contains punctures and/or reflector boundaries, that it is orientable, and that it contains at least one fibre-reversing path.
bn1	Indicates that the base orbifold contains punctures and/or reflector boundaries, that it is non-orientable, and that it contains no fibre-reversing paths.
bn2	Indicates that the base orbifold contains punctures and/or reflector boundaries, that it is non-orientable, and that its fibre-reversing paths correspond precisely to its orientation-reversing paths.
bn3	Indicates that the base orbifold contains punctures and/or reflector boundaries, that it is non-orientable, that it contains at least one fibre-reversing path, and that its fibre-reversing paths do not correspond precisely to its orientation-reversing paths.

Function Documentation

REGINA_API std::ostream& regina::operator<<	(	std::ostream &	out,
		const NSFSFibre &	f
	)

Writes the given fibre in human-readable format to the given output stream.

The fibre will be written in the format (alpha,beta) with no newline appended.

Parameters

out	the output stream to which to write.
f	the fibre to write.

Returns

the output stream out.