Regina Calculation Engine
Public Member Functions | Static Public Member Functions | List of all members
regina::BlockedSFSPair Class Reference

Represents a blocked pair of Seifert fibred spaces joined along a single connecting torus. More...

#include <subcomplex/blockedsfspair.h>

Inheritance diagram for regina::BlockedSFSPair:
regina::StandardTriangulation regina::Output< StandardTriangulation >

Public Member Functions

 ~BlockedSFSPair ()
 Destroys this structure and its constituent components. More...
 
const SatRegionregion (int which) const
 Returns details of one of the two bounded saturated regions that form this triangulation. More...
 
const Matrix2matchingReln () const
 Returns the matrix describing how the two saturated region boundaries are joined. More...
 
Manifoldmanifold () const override
 Returns the 3-manifold represented by this triangulation, if such a recognition routine has been implemented. More...
 
std::ostream & writeName (std::ostream &out) const override
 Writes the name of this triangulation as a human-readable string to the given output stream. More...
 
std::ostream & writeTeXName (std::ostream &out) const override
 Writes the name of this triangulation in TeX format to the given output stream. More...
 
void writeTextLong (std::ostream &out) const override
 Writes a detailed text representation of this object to the given output stream. More...
 
std::string name () const
 Returns the name of this specific triangulation as a human-readable string. More...
 
std::string TeXName () const
 Returns the name of this specific triangulation in TeX format. More...
 
virtual AbelianGrouphomology () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...
 
AbelianGrouphomologyH1 () const
 Returns the expected first homology group of this triangulation, if such a routine has been implemented. More...
 
virtual void writeTextShort (std::ostream &out) const
 Writes a short 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...
 

Static Public Member Functions

static BlockedSFSPairisBlockedSFSPair (Triangulation< 3 > *tri)
 Determines if the given triangulation is a blocked pair of Seifert fibred spaces, as described by this class. More...
 
static StandardTriangulationisStandardTriangulation (Component< 3 > *component)
 Determines whether the given component represents one of the standard triangulations understood by Regina. More...
 
static StandardTriangulationisStandardTriangulation (Triangulation< 3 > *tri)
 Determines whether the given triangulation represents one of the standard triangulations understood by Regina. More...
 

Detailed Description

Represents a blocked pair of Seifert fibred spaces joined along a single connecting torus.

This is a particular type of triangulation of a graph manifold, formed from two saturated regions whose torus boundaries are identified. An optional layering may be placed between the two torus boundaries to allow for a more interesting relationship between the boundary curves of each region. For more detail on saturated regions and their constituent saturated blocks, see the SatRegion class; for more detail on layerings, see the Layering class.

Each of the two saturated regions must have precisely one boundary component formed from just one saturated annulus, and this boundary may not be twisted (i.e., it must be a torus, not a Klein bottle). The way in which the boundaries from each region are identified is specified by a 2-by-2 matrix M, which expresses curves representing the fibres and base orbifold of the second region in terms of the first (see the page on Notation for Seifert fibred spaces for terminology).

More specifically, suppose that f0 and o0 are directed curves on the first region boundary and f1 and o1 are directed curves on the second region boundary, where f0 and f1 represent the fibres of each region and o0 and o1 represent the base orbifolds. Then the boundaries are joined according to the following relation:

    [f1]       [f0]
    [  ] = M * [  ]
    [o1]       [o0]

If a layering is present between the two boundaries, then the boundary curves are not identified directly. In this case, the matrix M shows how the layering relates the curves on each region boundary.

Note that the routines writeName() and writeTeXName() do not offer enough information to uniquely identify the triangulation, since this essentially requires 2-dimensional assemblings of saturated blocks. For full details, writeTextLong() may be used instead.

The optional StandardTriangulation routine manifold() is implemented for this class, but homology() is not.

Member Function Documentation

◆ detail()

std::string regina::Output< StandardTriangulation , 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.

◆ str()

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

Returns a short text representation of this object.

This text should be human-readable, should fit on a single line, and should not end with a newline. Where possible, it should use plain ASCII characters.

Python
In addition to str(), this is also used as the Python "stringification" function str().
Returns
a short text representation of this object.

◆ utf8()

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

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

Like str(), this text should be human-readable, should fit on a single line, and should not end with a newline. In addition, it may use unicode characters to make the output more pleasant to read. This string will be encoded in UTF-8.

Returns
a short text representation of this object.

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

Copyright © 1999-2021, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).