Regina Calculation Engine
Public Member Functions | List of all members
regina::GraphLoop Class Reference

Represents a closed graph manifold formed by joining a single bounded Seifert fibred space to itself along a torus. More...

#include <manifold/graphloop.h>

Inheritance diagram for regina::GraphLoop:
regina::Manifold regina::Output< Manifold >

Public Member Functions

 GraphLoop (SFSpace *sfs, long mat00, long mat01, long mat10, long mat11)
 Creates a new graph manifold as a self-identified Seifert fibred space. More...
 
 GraphLoop (SFSpace *sfs, const Matrix2 &matchingReln)
 Creates a new graph manifold as a self-identified Seifert fibred space. More...
 
 GraphLoop (const GraphLoop &cloneMe)
 Creates a clone of the given graph manifold. More...
 
 ~GraphLoop ()
 Destroys this structure along with the bounded Seifert fibred space and the matching matrix. More...
 
const SFSpacesfs () const
 Returns a reference to the bounded Seifert fibred space that is joined to itself. More...
 
const Matrix2matchingReln () const
 Returns a reference to the 2-by-2 matrix describing how the two boundary tori of the Seifert fibred space are joined together. More...
 
bool operator< (const GraphLoop &compare) const
 Determines in a fairly ad-hoc fashion whether this representation of this space is "smaller" than the given representation of the given space. More...
 
GraphLoopoperator= (const GraphLoop &cloneMe)
 Sets this to be a clone of the given graph manifold. More...
 
AbelianGrouphomology () const override
 Returns the first homology group of this 3-manifold, if such a routine has been implemented. More...
 
bool isHyperbolic () const override
 Returns whether or not this is a finite-volume hyperbolic manifold. More...
 
std::ostream & writeName (std::ostream &out) const override
 Writes the common name of this 3-manifold as a human-readable string to the given output stream. More...
 
std::ostream & writeTeXName (std::ostream &out) const override
 Writes the common name of this 3-manifold in TeX format to the given output stream. More...
 
std::string name () const
 Returns the common name of this 3-manifold as a human-readable string. More...
 
std::string TeXName () const
 Returns the common name of this 3-manifold in TeX format. More...
 
std::string structure () const
 Returns details of the structure of this 3-manifold that might not be evident from its common name. More...
 
virtual Triangulation< 3 > * construct () const
 Returns a triangulation of this 3-manifold, if such a construction has been implemented. More...
 
AbelianGrouphomologyH1 () const
 Returns the first homology group of this 3-manifold, if such a routine has been implemented. More...
 
bool operator< (const Manifold &compare) const
 Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold. More...
 
virtual std::ostream & writeStructure (std::ostream &out) const
 Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream. More...
 
void writeTextShort (std::ostream &out) const
 Writes a short text representation of this object to the given output stream. More...
 
void writeTextLong (std::ostream &out) const
 Writes a detailed text representation of this object to the given output stream. More...
 
std::string str () const
 Returns a short text representation of this object. More...
 
std::string utf8 () const
 Returns a short text representation of this object using unicode characters. More...
 
std::string detail () const
 Returns a detailed text representation of this object. More...
 

Detailed Description

Represents a closed graph manifold formed by joining a single bounded Seifert fibred space to itself along a torus.

The Seifert fibred space must have two boundary components, each a torus corresponding to a puncture in the base orbifold (with no fibre-reversing twist as one travels around the boundary).

The way in which the two torus boundaries are joined together is specified by a 2-by-2 matrix M. This matrix relates the locations of the fibres and base orbifold on the two boundary tori.

More specifically, suppose that f0 and o0 are generators of the first boundary torus, where f0 represents a directed fibre in the Seifert fibred space and o0 represents the oriented boundary of the base orbifold. Likewise, let f1 and o1 be generators of the second boundary torus representing a directed fibre and the oriented boundary of the base orbifold. Then the tori are joined together so that the curves f0, o0, f1 and o1 become related as follows:

    [f1]       [f0]
    [  ] = M * [  ]
    [o1]       [o0]

See the page on Notation for Seifert fibred spaces for details on some of the terminology used above.

The optional Manifold routine homology() is implemented, but the optional routine construct() is not.

Todo:
Optimise: Speed up homology calculations involving orientable base spaces by adding rank afterwards, instead of adding generators for genus into the presentation matrix.

Member Function Documentation

◆ detail()

std::string regina::Output< Manifold , false >::detail ( ) const
inherited

Returns a detailed text representation of this object.

This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.

Returns
a detailed text representation of this object.

◆ str()

std::string regina::Output< Manifold , false >::str ( ) const
inherited

Returns a short text representation of this object.

This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.

Python
In addition to str(), this is also used as the Python "stringification" function str().
Returns
a short text representation of this object.

◆ utf8()

std::string regina::Output< Manifold , false >::utf8 ( ) const
inherited

Returns a short text representation of this object using unicode characters.

Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.

Returns
a short text representation of this object.

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).