Public Member Functions

regina::NTorusBundle Class Reference
[Standard 3-Manifolds]

Represents a torus bundle over the circle. More...

#include <ntorusbundle.h>

Inheritance diagram for regina::NTorusBundle:
regina::NManifold regina::ShareableObject regina::boost::noncopyable

List of all members.

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 NMatrix2getMonodromy () const
 Returns the monodromy describing how the upper and lower torus boundaries are identified.
NAbelianGroupgetHomologyH1 () 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.

Detailed Description

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.

Test:
Tested in the test suite, though not exhaustively.
Todo:
Feature: Implement the == operator for finding conjugate and inverse matrices.

Constructor & Destructor Documentation

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.

Precondition:
The given matrix has determinant +1 or -1.
Parameters:
newMonodromydescribes 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 ]
 
Precondition:
The monodromy matrix formed from the given parameters has determinant +1 or -1.
Parameters:
mon00the (0,0) element of the monodromy matrix.
mon01the (0,1) element of the monodromy matrix.
mon10the (1,0) element of the monodromy matrix.
mon11the (1,1) element of the monodromy matrix.
regina::NTorusBundle::NTorusBundle ( const NTorusBundle cloneMe ) [inline]

Creates a clone of the given torus bundle.

Parameters:
cloneMethe torus bundle to clone.

Member Function Documentation

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.

Returns:
the first homology group of this 3-manifold, or 0 if the appropriate calculation routine has not yet been implemented.

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.

Returns:
the monodromy for this torus bundle.
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.

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

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.

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:
outthe output stream to which to write.
Returns:
a reference to the given output stream.

Implements regina::NManifold.


The documentation for this class was generated from the following file:

Copyright © 1999-2009, 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).