Represents a torus bundle over the circle. More...
#include <ntorusbundle.h>
Public Member Functions | |
NTorusBundle () | |
Creates a new trivial torus bundle over the circle. | |
NTorusBundle (const NMatrix2 &newMonodromy) | |
Creates a new torus bundle over the circle using the given monodromy. | |
NTorusBundle (long mon00, long mon01, long mon10, long mon11) | |
Creates a new torus bundle over the circle using the given monodromy. | |
NTorusBundle (const NTorusBundle &cloneMe) | |
Creates a clone of the given torus bundle. | |
const NMatrix2 & | getMonodromy () const |
Returns the monodromy describing how the upper and lower torus boundaries are identified. | |
NAbelianGroup * | getHomologyH1 () const |
Returns the first homology group of this 3-manifold, if such a routine has been implemented. | |
std::ostream & | writeName (std::ostream &out) const |
Writes the common name of this 3-manifold as a human-readable string to the given output stream. | |
std::ostream & | writeTeXName (std::ostream &out) const |
Writes the common name of this 3-manifold in TeX format to the given output stream. |
Represents a torus bundle over the circle.
This is expressed as the product of the torus and the interval, with the two torus boundaries identified according to some specified monodromy.
The monodromy is described by a 2-by-2 matrix M as follows. Let a and b be generating curves of the upper torus boundary, and let p and q be the corresponding curves on the lower torus boundary (so that a and p are parallel and b and q are parallel). Then we identify the torus boundaries so that, in additive terms:
[a] [p] [ ] = M * [ ] [b] [q]
All optional NManifold routines except for construct() are implemented for this class.
regina::NTorusBundle::NTorusBundle | ( | ) | [inline] |
Creates a new trivial torus bundle over the circle.
In other words, this routine creates a torus bundle with the identity monodromy.
regina::NTorusBundle::NTorusBundle | ( | const NMatrix2 & | newMonodromy | ) | [inline] |
Creates a new torus bundle over the circle using the given monodromy.
newMonodromy | describes precisely how the upper and lower torus boundaries are identified. See the class notes for details. |
regina::NTorusBundle::NTorusBundle | ( | long | mon00, | |
long | mon01, | |||
long | mon10, | |||
long | mon11 | |||
) | [inline] |
Creates a new torus bundle over the circle using the given monodromy.
The four elements of the monodromy matrix are passed separately. They combine to give the full monodromy matrix M as follows:
[ mon00 mon01 ] M = [ ] [ mon10 mon11 ]
mon00 | the (0,0) element of the monodromy matrix. | |
mon01 | the (0,1) element of the monodromy matrix. | |
mon10 | the (1,0) element of the monodromy matrix. | |
mon11 | the (1,1) element of the monodromy matrix. |
regina::NTorusBundle::NTorusBundle | ( | const NTorusBundle & | cloneMe | ) | [inline] |
Creates a clone of the given torus bundle.
cloneMe | the torus bundle to clone. |
NAbelianGroup* regina::NTorusBundle::getHomologyH1 | ( | ) | const [virtual] |
Returns the first homology group of this 3-manifold, if such a routine has been implemented.
If the calculation of homology has not yet been implemented for this 3-manifold then this routine will return 0.
The details of which 3-manifolds 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.
Reimplemented from regina::NManifold.
const NMatrix2 & regina::NTorusBundle::getMonodromy | ( | ) | const [inline] |
Returns the monodromy describing how the upper and lower torus boundaries are identified.
See the class notes for details.
std::ostream& regina::NTorusBundle::writeName | ( | std::ostream & | out | ) | const [virtual] |
Writes the common name of this 3-manifold as a human-readable string to the given output stream.
out | the output stream to which to write. |
Implements regina::NManifold.
std::ostream& regina::NTorusBundle::writeTeXName | ( | std::ostream & | out | ) | const [virtual] |
Writes the common name of this 3-manifold 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::NManifold.