Regina Calculation Engine
|
Represents a blocked Seifert fibred space. More...
#include <subcomplex/nblockedsfs.h>
Public Member Functions | |
~NBlockedSFS () | |
Destroys this structure and its constituent components. | |
const NSatRegion & | region () const |
Returns details of the single closed saturated region that fills this triangulation. | |
bool | isPluggedIBundle (std::string &name) const |
Determines whether this triangulation is a plugged thin I-bundle or a plugged thick I-bundle. | |
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 NBlockedSFS * | isBlockedSFS (NTriangulation *tri) |
Determines if the given triangulation is a blocked Seifert fibred space. |
Represents a blocked Seifert fibred space.
This is a particular type of triangulation of a closed Seifert fibred space, where this triangulation is formed from a single closed saturated region. A saturated region is in turn formed from saturated blocks by identifying their boundary annuli in pairs; see the NSatRegion class for details.
Note that the routines writeName() and writeTeXName() do not offer enough information to uniquely identify the triangulation, since this essentially requires a 2-dimensional assembling of saturated blocks. For full detail, writeTextLong() may be used instead.
The optional NStandardTriangulation routine getManifold() is implemented for this class, but getHomologyH1() is not.
Destroys this structure and its constituent components.
NManifold* regina::NBlockedSFS::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 NBlockedSFS* regina::NBlockedSFS::isBlockedSFS | ( | NTriangulation * | tri | ) | [static] |
Determines if the given triangulation is a blocked Seifert fibred space.
tri | the triangulation to examine. |
null
if the given triangulation is not a blocked Seifert fibred space. bool regina::NBlockedSFS::isPluggedIBundle | ( | std::string & | name | ) | const |
Determines whether this triangulation is a plugged thin I-bundle or a plugged thick I-bundle.
These structures are described in "Structures of small closed non-orientable 3-manifold triangulations", Benjamin A. Burton, J. Knot Theory Ramifications 16 (2007), 545--574.
name | used to return the name of the plugged thin/thick I-bundle, if the triangulation is of this form. If the triangulation is not of this form, this string is not touched. |
true
if this triangulation is indeed a plugged thin I-bundle or a plugged thick I-bundle. const NSatRegion & regina::NBlockedSFS::region | ( | ) | const [inline] |
Returns details of the single closed saturated region that fills this triangulation.
std::ostream& regina::NBlockedSFS::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::NBlockedSFS::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::NBlockedSFS::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.