Represents a layered lens space component of a triangulation. More...
#include <nlayeredlensspace.h>
Public Member Functions | |
virtual | ~NLayeredLensSpace () |
Destroys this lens space; note that the corresponding layered solid torus will also be destroyed. | |
NLayeredLensSpace * | clone () const |
Returns a newly created clone of this structure. | |
unsigned long | getP () const |
Returns the first parameter p of this lens space L(p,q). | |
unsigned long | getQ () const |
Returns the second parameter q of this lens space L(p,q). | |
const NLayeredSolidTorus & | getTorus () const |
Returns the layered solid torus to which the mobius strip is glued. | |
int | getMobiusBoundaryGroup () const |
Determines which edge of the layered solid torus is glued to the boundary of the mobius strip (i.e., the weight 2 edge of the degenerate (2,1,1) layered solid torus). | |
bool | isSnapped () const |
Determines if the layered solid torus that forms the basis for this lens space is snapped shut (folded closed without a twist). | |
bool | isTwisted () const |
Determines if the layered solid torus that forms the basis for this lens space is twisted shut (folded closed with a twist). | |
NManifold * | getManifold () const |
Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. | |
NAbelianGroup * | getHomologyH1 () const |
Returns the expected first homology group of this triangulation, if such a 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 NLayeredLensSpace * | isLayeredLensSpace (const NComponent *comp) |
Determines if the given triangulation component is a layered lens space. |
Represents a layered lens space component of a triangulation.
A layered lens space is considered to be any layered solid torus glued to a degenerate (2,1,1) layered solid torus (i.e., a one-triangle mobius strip). Note that the three possible gluing options represent the three possible ways of closing the initial torus - either twisting it shut (in one of two possible ways) or snapping it shut without any twist.
A layered lens space must contain at least one tetrahedron.
All optional NStandardTriangulation routines are implemented for this class.
regina::NLayeredLensSpace::~NLayeredLensSpace | ( | ) | [inline, virtual] |
Destroys this lens space; note that the corresponding layered solid torus will also be destroyed.
NLayeredLensSpace* regina::NLayeredLensSpace::clone | ( | ) | const |
Returns a newly created clone of this structure.
NAbelianGroup* regina::NLayeredLensSpace::getHomologyH1 | ( | ) | const [virtual] |
Returns the expected first homology group of this triangulation, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this triangulation then this routine will return 0.
This routine does not work by calling NTriangulation::getHomologyH1() on the associated real triangulation. Instead the homology is calculated directly from the known properties of this standard triangulation.
The details of which standard triangulations have homology calculation routines can be found in the notes for the corresponding subclasses of NStandardTriangulation. The default implementation of this routine returns 0.
The homology group will be newly allocated and must be destroyed by the caller of this routine.
If this NStandardTriangulation describes an entire NTriangulation (and not just a part thereof) then the results of this routine should be identical to the homology group obtained by calling NTriangulation::getHomologyH1() upon the associated real triangulation.
Reimplemented from regina::NStandardTriangulation.
NManifold* regina::NLayeredLensSpace::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.
int regina::NLayeredLensSpace::getMobiusBoundaryGroup | ( | ) | const [inline] |
Determines which edge of the layered solid torus is glued to the boundary of the mobius strip (i.e., the weight 2 edge of the degenerate (2,1,1) layered solid torus).
The return value will be one of the three top level tetrahedron edge groups in the layered solid torus; see NLayeredSolidTorus::getTopEdge() for further details about edge groups.
unsigned long regina::NLayeredLensSpace::getP | ( | ) | const [inline] |
Returns the first parameter p of this lens space L(p,q).
unsigned long regina::NLayeredLensSpace::getQ | ( | ) | const [inline] |
Returns the second parameter q of this lens space L(p,q).
const NLayeredSolidTorus & regina::NLayeredLensSpace::getTorus | ( | ) | const [inline] |
Returns the layered solid torus to which the mobius strip is glued.
static NLayeredLensSpace* regina::NLayeredLensSpace::isLayeredLensSpace | ( | const NComponent * | comp ) | [static] |
Determines if the given triangulation component is a layered lens space.
comp | the triangulation component to examine. |
null
if the given component is not a layered lens space. bool regina::NLayeredLensSpace::isSnapped | ( | ) | const [inline] |
Determines if the layered solid torus that forms the basis for this lens space is snapped shut (folded closed without a twist).
true
if and only if the torus is snapped shut. bool regina::NLayeredLensSpace::isTwisted | ( | ) | const [inline] |
Determines if the layered solid torus that forms the basis for this lens space is twisted shut (folded closed with a twist).
true
if and only if the torus is twisted shut. std::ostream& regina::NLayeredLensSpace::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::NLayeredLensSpace::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::NLayeredLensSpace::writeTextLong | ( | std::ostream & | out ) | const [inline, 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.