Represents a blocked pair of Seifert fibred spaces joined along a single connecting torus. More...
#include <nblockedsfspair.h>
Public Member Functions | |
~NBlockedSFSPair () | |
Destroys this structure and its constituent components. | |
const NSatRegion & | region (int which) const |
Returns details of one of the two bounded saturated regions that form this triangulation. | |
const NMatrix2 & | matchingReln () const |
Returns the matrix describing how the two saturated region boundaries are joined. | |
NManifold * | getManifold () const |
Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. | |
std::ostream & | writeName (std::ostream &out) const |
Writes the name of this triangulation as a human-readable string to the given output stream. | |
std::ostream & | writeTeXName (std::ostream &out) const |
Writes the name of this triangulation in TeX format to the given output stream. | |
void | writeTextLong (std::ostream &out) const |
Writes this object in long text format to the given output stream. | |
Static Public Member Functions | |
static NBlockedSFSPair * | isBlockedSFSPair (NTriangulation *tri) |
Determines if the given triangulation is a blocked pair of Seifert fibred spaces, as described by this class. |
Represents a blocked pair of Seifert fibred spaces joined along a single connecting torus.
This is a particular type of triangulation of a graph manifold, formed from two saturated regions whose torus boundaries are identified. An optional layering may be placed between the two torus boundaries to allow for a more interesting relationship between the boundary curves of each region. For more detail on saturated regions and their constituent saturated blocks, see the NSatRegion class; for more detail on layerings, see the NLayering class.
Each of the two saturated regions must have precisely one boundary component formed from just one saturated annulus, and this boundary may not be twisted (i.e., it must be a torus, not a Klein bottle). The way in which the boundaries from each region are identified is specified by a 2-by-2 matrix M, which expresses curves representing the fibres and base orbifold of the second region in terms of the first (see the page on Notation for Seifert fibred spaces for terminology).
More specifically, suppose that f0 and o0 are directed curves on the first region boundary and f1 and o1 are directed curves on the second region boundary, where f0 and f1 represent the fibres of each region and o0 and o1 represent the base orbifolds. Then the boundaries are joined according to the following relation:
[f1] [f0] [ ] = M * [ ] [o1] [o0]
If a layering is present between the two boundaries, then the boundary curves are not identified directly. In this case, the matrix M shows how the layering relates the curves on each region boundary.
Note that the routines writeName() and writeTeXName() do not offer enough information to uniquely identify the triangulation, since this essentially requires 2-dimensional assemblings of saturated blocks. For full details, writeTextLong() may be used instead.
The optional NStandardTriangulation routine getManifold() is implemented for this class, but getHomologyH1() is not.
regina::NBlockedSFSPair::~NBlockedSFSPair | ( | ) |
Destroys this structure and its constituent components.
NManifold* regina::NBlockedSFSPair::getManifold | ( | ) | const [virtual] |
Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented.
If the 3-manifold cannot be recognised then this routine will return 0.
The details of which standard triangulations have 3-manifold recognition routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0.
It is expected that the number of triangulations whose underlying 3-manifolds can be recognised will grow between releases.
The 3-manifold will be newly allocated and must be destroyed by the caller of this routine.
Reimplemented from regina::NStandardTriangulation.
static NBlockedSFSPair* regina::NBlockedSFSPair::isBlockedSFSPair | ( | NTriangulation * | tri ) | [static] |
Determines if the given triangulation is a blocked pair of Seifert fibred spaces, as described by this class.
tri | the triangulation to examine. |
null
if the given triangulation is not of this form. const NMatrix2 & regina::NBlockedSFSPair::matchingReln | ( | ) | const [inline] |
Returns the matrix describing how the two saturated region boundaries are joined.
Note that if a layering is placed between the two region boundaries, then any changes to the boundary relationships caused by the layering are included in this matrix.
See the class notes above for precise information on how this matrix is presented.
const NSatRegion & regina::NBlockedSFSPair::region | ( | int | which ) | const [inline] |
Returns details of one of the two bounded saturated regions that form this triangulation.
See the class notes above for further information.
which | 0 if the first region should be returned, or 1 if the second region should be returned. |
std::ostream& regina::NBlockedSFSPair::writeName | ( | std::ostream & | out ) | const [virtual] |
Writes the name of this triangulation as a human-readable string to the given output stream.
out | the output stream to which to write. |
Implements regina::NStandardTriangulation.
std::ostream& regina::NBlockedSFSPair::writeTeXName | ( | std::ostream & | out ) | const [virtual] |
Writes the name of this triangulation in TeX format to the given output stream.
No leading or trailing dollar signs will be included.
out | the output stream to which to write. |
Implements regina::NStandardTriangulation.
void regina::NBlockedSFSPair::writeTextLong | ( | std::ostream & | out ) | const [virtual] |
Writes this object in long text format to the given output stream.
The output should provided the user with all the information they could want. The output should end with a newline.
The default implementation of this routine merely calls writeTextShort() and adds a newline.
out | the output stream to which to write. |
Reimplemented from regina::ShareableObject.