Regina Calculation Engine

Represents a closed graph manifold formed by joining three bounded Seifert fibred spaces along their torus boundaries. More...
#include <manifold/ngraphtriple.h>
Public Member Functions  
NGraphTriple (NSFSpace *end0, NSFSpace *centre, NSFSpace *end1, const NMatrix2 &matchingReln0, const NMatrix2 &matchingReln1)  
Creates a new graph manifold from three bounded Seifert fibred spaces, as described in the class notes. More...  
~NGraphTriple ()  
Destroys this structure along with the component Seifert fibred spaces and matching matrices. More...  
const NSFSpace &  end (unsigned which) const 
Returns a reference to one of the two end spaces. More...  
const NSFSpace &  centre () const 
Returns a reference to the central space. More...  
const NMatrix2 &  matchingReln (unsigned which) const 
Returns a reference to the 2by2 matrix describing how the two requested bounded Seifert fibred spaces are joined together. More...  
bool  operator< (const NGraphTriple &compare) const 
Determines in a fairly adhoc fashion whether this representation of this space is "smaller" than the given representation of the given space. More...  
NAbelianGroup *  homology () const 
Returns the first homology group of this 3manifold, if such a routine has been implemented. More...  
bool  isHyperbolic () const 
Returns whether or not this is a finitevolume hyperbolic manifold. More...  
std::ostream &  writeName (std::ostream &out) const 
Writes the common name of this 3manifold as a humanreadable string to the given output stream. More...  
std::ostream &  writeTeXName (std::ostream &out) const 
Writes the common name of this 3manifold in TeX format to the given output stream. More...  
std::string  name () const 
Returns the common name of this 3manifold as a humanreadable string. More...  
REGINA_DEPRECATED std::string  getName () const 
Deprecated routine that returns the common name of this 3manifold as a humanreadable string. More...  
std::string  TeXName () const 
Returns the common name of this 3manifold in TeX format. More...  
REGINA_DEPRECATED std::string  getTeXName () const 
Deprecated routine that returns the common name of this 3manifold in TeX format. More...  
std::string  structure () const 
Returns details of the structure of this 3manifold that might not be evident from its common name. More...  
REGINA_DEPRECATED std::string  getStructure () const 
Deprecated routine that returns details of the structure of this 3manifold that might not be evident from its common name. More...  
virtual NTriangulation *  construct () const 
Returns a triangulation of this 3manifold, if such a construction has been implemented. More...  
NAbelianGroup *  homologyH1 () const 
Returns the first homology group of this 3manifold, if such a routine has been implemented. More...  
REGINA_DEPRECATED NAbelianGroup *  getHomologyH1 () const 
Deprecated routine that returns the first homology group of this 3manifold, if such a routine has been implemented. More...  
bool  operator< (const NManifold &compare) const 
Determines in a fairly adhoc fashion whether this representation of this 3manifold is "smaller" than the given representation of the given 3manifold. More...  
virtual std::ostream &  writeStructure (std::ostream &out) const 
Writes details of the structure of this 3manifold 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...  
REGINA_DEPRECATED std::string  toString () const 
A deprecated alias for str(). More...  
REGINA_DEPRECATED std::string  toStringLong () const 
A deprecated alias for detail(). More...  
Represents a closed graph manifold formed by joining three bounded Seifert fibred spaces along their torus boundaries.
There must be one Seifert fibred space at either end, each with a single torus boundary (corresponding to a single puncture in the base orbifold, with no fibrereversing twist around this puncture). Each of these end spaces is joined to the space in the centre, which has two disjoint torus boundaries (corresponding to two punctures in the base orbifold, again with no fibrereversing twists around these punctures).
This configuration is illustrated in the diagram below. The large boxes represent the bounded Seifert fibred spaces, and the small tunnels show how their boundaries are joined.
/\ /\ /\        End space 0  Central space  End space 1            \/ \/ \/
The way in which each pair of spaces is joined is specified by a 2by2 matrix. This matrix expresses the locations of the fibres and base orbifold of the corresponding end space in terms of the central space. Note that these are not the same matrices that appear in the manifold name in the census data files! See the warning below.
More specifically, consider the matrix M that describes the joining of the central space and the first end space (marked above as end space 0). Suppose that f and o are generators of the common boundary torus, where f represents a directed fibre in the central space and o represents the oriented boundary of the corresponding base orbifold. Likewise, let f0 and o0 be generators of the common boundary torus representing a directed fibre and the base orbifold of the first end space. Then the curves f, o, f0 and o0 are related as follows:
[f0] [f ] [ ] = M * [ ] [o0] [o ]
Likewise, let matrix M' describe the joining of the central space and the second end space (marked in the diagram above as end space 1). Let f' and o' be curves on the common boundary torus representing the fibres and the base orbifold of the central space, and let f1 and o1 be curves on this same torus representing the fibres and the base orbifold of the second end space. Then the curves f', o', f1 and o1 are related as follows:
[f1] [f'] [ ] = M' * [ ] [o1] [o']
See the page on Notation for Seifert fibred spaces for details on some of the terminology used above.
The optional NManifold routine homology() is implemented, but the optional routine construct() is not.

inline 
Creates a new graph manifold from three bounded Seifert fibred spaces, as described in the class notes.
The three Seifert fibred spaces and both 2by2 matching matrices are passed separately.
Note that the new object will take ownership of the three given Seifert fibred spaces, and when this object is destroyed the Seifert fibred spaces will be destroyed also.
end0  the first end space, as described in the class notes. 
centre  the central space, as described in the class notes. 
end1  the second end space, as described in the class notes. 
matchingReln0  the 2by2 matching matrix that specifies how spaces end0 and centre are joined. 
matchingReln1  the 2by2 matching matrix that specifies how spaces end1 and centre are joined. 
regina::NGraphTriple::~NGraphTriple  (  ) 
Destroys this structure along with the component Seifert fibred spaces and matching matrices.

inline 
Returns a reference to the central space.
This is the Seifert fibred space with two boundary components, to which the two end spaces are joined. See the class notes for further discussion.

inlinevirtualinherited 
Returns a triangulation of this 3manifold, if such a construction has been implemented.
If no construction routine has yet been implemented for this 3manifold (for instance, if this 3manifold is a Seifert fibred space with sufficiently many exceptional fibres) then this routine will return 0.
The details of which 3manifolds have construction routines can be found in the notes for the corresponding subclasses of NManifold. The default implemention of this routine returns 0.
Reimplemented in regina::NSFSpace, regina::NSnapPeaCensusManifold, regina::NLensSpace, and regina::NSimpleSurfaceBundle.

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 humanreadable, 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.

inline 
Returns a reference to one of the two end spaces.
These are the Seifert fibred spaces with just one boundary component, to be joined to the central space. See the class notes for further discussion.
which  0 if the first end space is to be returned, or 1 if the second end space is to be returned. 

inlineinherited 
Deprecated routine that returns the first homology group of this 3manifold, if such a routine has been implemented.

inlineinherited 
Deprecated routine that returns the common name of this 3manifold as a humanreadable string.

inlineinherited 
Deprecated routine that returns details of the structure of this 3manifold that might not be evident from its common name.

inlineinherited 
Deprecated routine that returns the common name of this 3manifold in TeX format.

virtual 
Returns the first homology group of this 3manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3manifold then this routine will return 0.
The details of which 3manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of NManifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
This routine can also be accessed via the alias homologyH1() (a name that is more specific, but a little longer to type).
Reimplemented from regina::NManifold.

inlineinherited 
Returns the first homology group of this 3manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3manifold then this routine will return 0.
The details of which 3manifolds have homology calculation routines can be found in the notes for the corresponding subclasses of NManifold. The default implemention of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
This routine can also be accessed via the alias homology() (a name that is less specific, but a little easier to type).

inlinevirtual 
Returns whether or not this is a finitevolume hyperbolic manifold.
true
if this is a finitevolume hyperbolic manifold, or false
if not. Implements regina::NManifold.

inline 
Returns a reference to the 2by2 matrix describing how the two requested bounded Seifert fibred spaces are joined together.
See the class notes for details on precisely how these matrices are represented.
The argument which indicates which particular join should be examined. A value of 0 denotes the join between the central space and the first end space (corresponding to matrix M in the class notes), whereas a value of 1 denotes the join between the central space and the second end space (corresponding to matrix M' in the class notes).
which  indicates which particular join should be examined; this should be 0 or 1 as described above. 

inherited 
Returns the common name of this 3manifold as a humanreadable string.

inherited 
Determines in a fairly adhoc fashion whether this representation of this 3manifold is "smaller" than the given representation of the given 3manifold.
The ordering imposed on 3manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina.
The ordering also depends on the particular representation of the 3manifold that is used. As an example, different representations of the same Seifert fibred space might well be ordered differently.
All that this routine really offers is a welldefined way of ordering 3manifold representations.
compare  the 3manifold representation with which this will be compared. 
true
if and only if this is "smaller" than the given 3manifold representation. bool regina::NGraphTriple::operator<  (  const NGraphTriple &  compare  )  const 
Determines in a fairly adhoc fashion whether this representation of this space is "smaller" than the given representation of the given space.
The ordering imposed on graph manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina. It also depends upon the particular representation, so that different representations of the same space may be ordered differently.
All that this routine really offers is a welldefined way of ordering graph manifold representations.
compare  the representation with which this will be compared. 
true
if and only if this is "smaller" than the given graph manifold representation.

inherited 
Returns a short text representation of this object.
This text should be humanreadable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.
__str__()
.

inherited 
Returns details of the structure of this 3manifold that might not be evident from its common name.
For instance, for an orbit space S^3/G this routine might return the full Seifert structure.
This routine may return the empty string if no additional details are deemed necessary.

inherited 
Returns the common name of this 3manifold in TeX format.
No leading or trailing dollar signs will be included.

inherited 
A deprecated alias for str().

inherited 
A deprecated alias for detail().

inherited 
Returns a short text representation of this object using unicode characters.
Like str(), this text should be humanreadable, 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 UTF8.

virtual 
Writes the common name of this 3manifold as a humanreadable string to the given output stream.
None
.out  the output stream to which to write. 
Implements regina::NManifold.

inlinevirtualinherited 
Writes details of the structure of this 3manifold that might not be evident from its common name to the given output stream.
For instance, for an orbit space S^3/G this routine might write the full Seifert structure.
This routine may write nothing if no additional details are deemed necessary. The default implementation of this routine behaves in this way.
None
.out  the output stream to which to write. 
Reimplemented in regina::NSFSpace, and regina::NSnapPeaCensusManifold.

virtual 
Writes the common name of this 3manifold in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
None
.out  the output stream to which to write. 
Implements regina::NManifold.

inlineinherited 
Writes a detailed text representation of this object to the given output stream.
Subclasses must not override this routine. They should override writeName() and writeStructure() instead.
out  the output stream to which to write. 

inlineinherited 
Writes a short text representation of this object to the given output stream.
Subclasses must not override this routine. They should override writeName() instead.
out  the output stream to which to write. 