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

#include <manifold/torusbundle.h>

Inheritance diagram for regina::TorusBundle:

Public Member Functions
	TorusBundle ()
	Creates a new trivial torus bundle over the circle. More...

	TorusBundle (const Matrix2 &newMonodromy)
	Creates a new torus bundle over the circle using the given monodromy. More...

	TorusBundle (long mon00, long mon01, long mon10, long mon11)
	Creates a new torus bundle over the circle using the given monodromy. More...

	TorusBundle (const TorusBundle &)=default
	Creates a new copy of the given torus bundle. More...

const Matrix2 &	monodromy () const
	Returns the monodromy describing how the upper and lower torus boundaries are identified. More...

TorusBundle &	operator= (const TorusBundle &)=default
	Sets this to be a copy of the given torus bundle. More...

void	swap (TorusBundle &other) noexcept
	Swaps the contents of this and the given torus bundle. More...

bool	operator== (const TorusBundle &compare) const
	Determines whether this and the given object contain precisely the same presentations of the same torus bundle. More...

bool	operator!= (const TorusBundle &compare) const
	Determines whether this and the given object do not contain precisely the same presentations of the same torus bundle. More...

AbelianGroup	homology () const override
	Returns the first homology group of this 3-manifold, if such a routine has been implemented. More...

bool	isHyperbolic () const override
	Returns whether or not this is a finite-volume hyperbolic manifold. More...

std::ostream &	writeName (std::ostream &out) const override
	Writes the common name of this 3-manifold as a human-readable string to the given output stream. More...

std::ostream &	writeTeXName (std::ostream &out) const override
	Writes the common name of this 3-manifold in TeX format to the given output stream. More...

std::string	name () const
	Returns the common name of this 3-manifold as a human-readable string. More...

std::string	texName () const
	Returns the common name of this 3-manifold in TeX format. More...

std::string	TeXName () const
	Deprecated routine that returns the common name of this 3-manifold in TeX format. More...

std::string	structure () const
	Returns details of the structure of this 3-manifold that might not be evident from its common name. More...

virtual Triangulation< 3 >	construct () const
	Returns a triangulation of this 3-manifold, if such a construction has been implemented. More...

AbelianGroup	homologyH1 () const
	A deprecated alias for homology(). More...

bool	operator< (const Manifold &compare) const
	Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold. More...

virtual std::ostream &	writeStructure (std::ostream &out) const
	Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream. More...

void	writeTextShort (std::ostream &out) const
	Writes a short text representation of this object to the given output stream. More...

void	writeTextLong (std::ostream &out) const
	Writes a detailed text representation of this object to the given output stream. More...

std::string	str () const
	Returns a short text representation of this object. More...

std::string	utf8 () const
	Returns a short text representation of this object using unicode characters. More...

std::string	detail () const
	Returns a detailed text representation of this object. More...

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 Manifold routines except for construct() are implemented for this class.

This class supports copying but does not implement separate move operations, since its internal data is so small that copying is just as efficient. It implements the C++ Swappable requirement via its own member and global swap() functions, for consistency with the other manifold classes.

Todo:: Feature: Implement the == operator for finding conjugate and inverse matrices.

Constructor & Destructor Documentation

◆ TorusBundle() [1/4]

regina::TorusBundle::TorusBundle ( )

inline

Creates a new trivial torus bundle over the circle.

In other words, this routine creates a torus bundle with the identity monodromy.

◆ TorusBundle() [2/4]

regina::TorusBundle::TorusBundle ( const Matrix2 & newMonodromy )

inline

Creates a new torus bundle over the circle using the given monodromy.

Precondition: The given matrix has determinant +1 or -1.

Parameters

newMonodromy describes precisely how the upper and lower torus boundaries are identified. See the class notes for details.

◆ TorusBundle() [3/4]

regina::TorusBundle::TorusBundle	(	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

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.

◆ TorusBundle() [4/4]

regina::TorusBundle::TorusBundle ( const TorusBundle & )

default

Creates a new copy of the given torus bundle.

Member Function Documentation

◆ construct()

virtual Triangulation< 3 > regina::Manifold::construct ( ) const

virtualinherited

Returns a triangulation of this 3-manifold, if such a construction has been implemented.

For details of which types of 3-manifolds have implemented this routine, see the class notes for each corresponding subclasses of Manifold.

The default implemention of this routine just throws a NotImplemented exception.

Exceptions

NotImplemented	explicit construction has not yet been implemented for this particular 3-manifold.
FileError	the construction needs to be read from file (as opposed to computed on the fly), but the file is inaccessible or its contents cannot be read and parsed correctly. Currently this can only happen for the subclass SnapPeaCensusManifold, which reads its triangulations from the SnapPea census databases that are installed with Regina.

Returns: a triangulation of this 3-manifold, if this construction has been implemented.

Reimplemented in regina::LensSpace, regina::SFSpace, regina::SimpleSurfaceBundle, and regina::SnapPeaCensusManifold.

◆ detail()

std::string regina::Output< Manifold , false >::detail ( ) const

inherited

Returns a detailed text representation of this object.

This text may span many lines, and should provide the user with all the information they could want. It should be human-readable, should not contain extremely long lines (which cause problems for users reading the output in a terminal), and should end with a final newline. There are no restrictions on the underlying character set.

Returns: a detailed text representation of this object.

◆ homology()

AbelianGroup regina::TorusBundle::homology ( ) const

overridevirtual

Returns the first homology group of this 3-manifold, if such a routine has been implemented.

For details of which types of 3-manifolds have implemented this routine, see the class notes for each corresponding subclasses of Manifold.

The default implemention of this routine just throws a NotImplemented exception.

This routine can also be accessed via the alias homologyH1() (a name that is more specific, but a little longer to type).

Exceptions

NotImplemented	homology calculation has not yet been implemented for this particular 3-manifold.
FileError	the homology needs to be read from file (as opposed to computed), but the file is inaccessible or its contents cannot be read and parsed correctly. Currently this can only happen for the subclass SnapPeaCensusManifold, which reads its results from the SnapPea census databases that are installed with Regina.

Returns: the first homology group of this 3-manifold, if this functionality has been implemented.

Reimplemented from regina::Manifold.

◆ homologyH1()

AbelianGroup regina::Manifold::homologyH1 ( ) const

inlineinherited

A deprecated alias for homology().

Deprecated:: This routine can be accessed by the simpler name homology().

Exceptions

NotImplemented	homology calculation has not yet been implemented for this particular 3-manifold.
the	homology needs to be read from file (as opposed to computed), but the file is inaccessible or its contents cannot be read and parsed correctly. Currently this can only happen for the subclass SnapPeaCensusManifold, which reads its results from the SnapPea census databases that are installed with Regina.

Returns: the first homology group of this 3-manifold, if this functionality has been implemented.

◆ isHyperbolic()

bool regina::TorusBundle::isHyperbolic ( ) const

inlineoverridevirtual

Returns whether or not this is a finite-volume hyperbolic manifold.

Returns: true if this is a finite-volume hyperbolic manifold, or false if not.

Implements regina::Manifold.

◆ monodromy()

const Matrix2 & regina::TorusBundle::monodromy ( ) 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.

◆ name()

std::string regina::Manifold::name ( ) const

inherited

Returns the common name of this 3-manifold as a human-readable string.

Returns: the common name of this 3-manifold.

◆ operator!=()

bool regina::TorusBundle::operator!= ( const TorusBundle & compare ) const

inline

Determines whether this and the given object do not contain precisely the same presentations of the same torus bundle.

This routine does not test for homeomorphism; instead it compares the specific monodromies. If you have two objects that represent same torus bundle using two different monodromies, they will be treated as not equal by this routine.

Parameters

compare the presentation with which this will be compared.

Returns: true if and only if this and the given object do not contain identical presentations of the same torus bundle.

◆ operator<()

bool regina::Manifold::operator< ( const Manifold & compare ) const

inherited

Determines in a fairly ad-hoc fashion whether this representation of this 3-manifold is "smaller" than the given representation of the given 3-manifold.

The ordering imposed on 3-manifolds is purely aesthetic on the part of the author, and is subject to change in future versions of Regina.

The ordering also depends on the particular representation of the 3-manifold that is used. As an example, different representations of the same Seifert fibred space might well be ordered differently.

All that this routine really offers is a well-defined way of ordering 3-manifold representations.

Warning: Currently this routine is only implemented in full for closed 3-manifolds. For most classes of bounded 3-manifolds, this routine simply compares the strings returned by name().

Parameters

compare the 3-manifold representation with which this will be compared.

Returns: true if and only if this is "smaller" than the given 3-manifold representation.

◆ operator=()

TorusBundle & regina::TorusBundle::operator= ( const TorusBundle & )

default

Sets this to be a copy of the given torus bundle.

Returns: a reference to this torus bundle.

◆ operator==()

bool regina::TorusBundle::operator== ( const TorusBundle & compare ) const

inline

Determines whether this and the given object contain precisely the same presentations of the same torus bundle.

This routine does not test for homeomorphism; instead it compares the specific monodromies. If you have two objects that represent same torus bundle using two different monodromies, they will be treated as not equal by this routine.

Parameters

compare the presentation with which this will be compared.

Returns: true if and only if this and the given object contain identical presentations of the same torus bundle.

◆ str()

std::string regina::Output< Manifold , false >::str ( ) const

inherited

Returns a short text representation of this object.

This text should be human-readable, should use plain ASCII characters where possible, and should not contain any newlines.

Within these limits, this short text ouptut should be as information-rich as possible, since in most cases this forms the basis for the Python str() and repr() functions.

Python: The Python "stringification" function str() will use precisely this function, and for most classes the Python repr() function will incorporate this into its output.

Returns: a short text representation of this object.

◆ structure()

std::string regina::Manifold::structure ( ) const

inherited

Returns details of the structure of this 3-manifold that might not be evident from its common name.

For instance, for an orbit space S^3/G this routine might return the full Seifert structure.

This routine may return the empty string if no additional details are deemed necessary.

Returns: a string describing additional structural details.

◆ swap()

void regina::TorusBundle::swap ( TorusBundle & other )

inlinenoexcept

Swaps the contents of this and the given torus bundle.

Parameters

other the torus bundle whose contents should be swapped with this.

◆ texName()

std::string regina::Manifold::texName ( ) const

inherited

Returns the common name of this 3-manifold in TeX format.

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.

Returns: the common name of this 3-manifold in TeX format.

◆ TeXName()

std::string regina::Manifold::TeXName ( ) const

inlineinherited

Deprecated routine that returns the common name of this 3-manifold in TeX format.

Deprecated:: This routine has been renamed to texName().

Returns: the common name of this 3-manifold in TeX format.

◆ utf8()

std::string regina::Output< Manifold , false >::utf8 ( ) const

inherited

Returns a short text representation of this object using unicode characters.

Like str(), this text should be human-readable, should not contain any newlines, and (within these constraints) should be as information-rich as is reasonable.

Unlike str(), this function may use unicode characters to make the output more pleasant to read. The string that is returned will be encoded in UTF-8.

Returns: a short text representation of this object.

◆ writeName()

std::ostream & regina::TorusBundle::writeName ( std::ostream & out ) const

overridevirtual

Writes the common name of this 3-manifold as a human-readable string to the given output stream.

Python: Not present; instead use the variant name() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Implements regina::Manifold.

◆ writeStructure()

std::ostream & regina::Manifold::writeStructure ( std::ostream & out ) const

inlinevirtualinherited

Writes details of the structure of this 3-manifold that might not be evident from its common name to the given output stream.

For instance, for an orbit space S^3/G this routine might write the full Seifert structure.

This routine may write nothing if no additional details are deemed necessary. The default implementation of this routine behaves in this way.

Python: Not present; instead use the variant structure() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Reimplemented in regina::SFSpace, and regina::SnapPeaCensusManifold.

◆ writeTeXName()

std::ostream & regina::TorusBundle::writeTeXName ( std::ostream & out ) const

overridevirtual

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: Not present; instead use the variant texName() that takes no arguments and returns a string.

Parameters

out	the output stream to which to write.

Returns: a reference to the given output stream.

Implements regina::Manifold.

◆ writeTextLong()

void regina::Manifold::writeTextLong ( std::ostream & out ) const

inlineinherited

Writes a detailed text representation of this object to the given output stream.

Subclasses must not override this routine. They should override writeName() and writeStructure() instead.

Python: Not present; use detail() instead.

Parameters

out	the output stream to which to write.

◆ writeTextShort()

void regina::Manifold::writeTextShort ( std::ostream & out ) const

inlineinherited

Writes a short text representation of this object to the given output stream.

Subclasses must not override this routine. They should override writeName() instead.

Python: Not present; use str() instead.

Parameters

out	the output stream to which to write.

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

manifold/torusbundle.h

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ TorusBundle() [1/4]

◆ TorusBundle() [2/4]

◆ TorusBundle() [3/4]

◆ TorusBundle() [4/4]

Member Function Documentation

◆ construct()

◆ detail()

◆ homology()

◆ homologyH1()

◆ isHyperbolic()

◆ monodromy()

◆ name()

◆ operator!=()

◆ operator<()

◆ operator=()

◆ operator==()

◆ str()

◆ structure()

◆ swap()

◆ texName()

◆ TeXName()

◆ utf8()

◆ writeName()

◆ writeStructure()

◆ writeTeXName()

◆ writeTextLong()

◆ writeTextShort()