regina::NLayeredLensSpace Class Reference
[Standard Triangulations and Subcomplexes]

Represents a layered lens space component of a triangulation. More...

#include <nlayeredlensspace.h>

Inheritance diagram for regina::NLayeredLensSpace:

regina::NStandardTriangulation regina::ShareableObject regina::boost::noncopyable

List of all members.

Public Member Functions

virtual ~NLayeredLensSpace ()
 Destroys this lens space; note that the corresponding layered solid torus will also be destroyed.
NLayeredLensSpaceclone () 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).
NManifoldgetManifold () const
 Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented.
NAbelianGroupgetHomologyH1 () 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.


Detailed Description

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.


Constructor & Destructor Documentation

regina::NLayeredLensSpace::~NLayeredLensSpace (  )  [inline, virtual]

Destroys this lens space; note that the corresponding layered solid torus will also be destroyed.


Member Function Documentation

NLayeredLensSpace* regina::NLayeredLensSpace::clone (  )  const

Returns a newly created clone of this structure.

Returns:
a newly created clone.

unsigned long regina::NLayeredLensSpace::getP (  )  const [inline]

Returns the first parameter p of this lens space L(p,q).

Returns:
the first parameter p.

unsigned long regina::NLayeredLensSpace::getQ (  )  const [inline]

Returns the second parameter q of this lens space L(p,q).

Returns:
the second parameter q.

const NLayeredSolidTorus & regina::NLayeredLensSpace::getTorus (  )  const [inline]

Returns the layered solid torus to which the mobius strip is glued.

Returns:
the layered solid torus.

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.

Returns:
the top level edge group of the layered solid torus to which the mobius strip boundary is glued.

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).

Returns:
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).

Returns:
true if and only if the torus is twisted shut.

static NLayeredLensSpace* regina::NLayeredLensSpace::isLayeredLensSpace ( const NComponent comp  )  [static]

Determines if the given triangulation component is a layered lens space.

Parameters:
comp the triangulation component to examine.
Returns:
a newly created structure containing details of the layered lens space, or null if the given component is not a layered lens space.

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.

Returns:
the underlying 3-manifold.

Reimplemented from regina::NStandardTriangulation.

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.

Returns:
the first homology group of this triangulation, or 0 if the appropriate calculation routine has not yet been implemented.

Reimplemented from regina::NStandardTriangulation.

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.

Python:
The parameter out does not exist; standard output will be used.
Parameters:
out the output stream to which to write.
Returns:
a reference to the given output stream.

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.

Warning:
The behaviour of this routine has changed as of Regina 4.3; in earlier versions, leading and trailing dollar signs were provided.
Python:
The parameter out does not exist; standard output will be used.
Parameters:
out the output stream to which to write.
Returns:
a reference to the given output stream.

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.

Python:
The parameter out does not exist; standard output will be used.
Parameters:
out the output stream to which to write.

Reimplemented from regina::ShareableObject.


The documentation for this class was generated from the following file:
Copyright © 1999-2006, Ben Burton
This software is released under the GNU General Public License.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).