Regina Calculation Engine
Classes | Enumerations | Functions
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

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
outthe output stream to which to write.
fthe fibre to write.
Returns
the output stream out.

Copyright © 1999-2014, 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@debian.org).