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

A saturated block that is a layered solid torus. More...

#include <nsatblocktypes.h>

Inheritance diagram for regina::NSatLST:
regina::NSatBlock regina::ShareableObject regina::boost::noncopyable

List of all members.

Public Member Functions

 NSatLST (const NSatLST &cloneMe)
 Constructs a clone of the given block structure.
 ~NSatLST ()
 Destroys this structure and its internal components.
const NLayeredSolidToruslst () const
 Returns details of the layered solid torus that this block represents.
NPerm roles () const
 Describes how the layered solid torus is attached to the boundary annulus.
virtual NSatBlockclone () const
 Returns a newly created clone of this saturated block structure.
virtual void adjustSFS (NSFSpace &sfs, bool reflect) const
 Adjusts the given Seifert fibred space to insert the contents of this saturated block.
virtual void transform (const NTriangulation *originalTri, const NIsomorphism *iso, NTriangulation *newTri)
 Adjusts the structure of this block according to the given isomorphism between triangulations.
virtual void writeTextShort (std::ostream &out) const
 Writes this object in short text format to the given output stream.
virtual void writeAbbr (std::ostream &out, bool tex=false) const
 Writes an abbreviated name or symbol for this block to the given output stream.

Static Public Member Functions

static NSatLSTisBlockLST (const NSatAnnulus &annulus, TetList &avoidTets)
 Determines whether the given annulus is a boundary annulus for a block of this type (layered solid torus).

Detailed Description

A saturated block that is a layered solid torus.

See the NLayeredSolidTorus class for details.

The three boundary edges of the layered solid torus are attached to the vertical, horizontal and diagonal edges of the boundary annulus; see the NSatAnnulus class notes for details on precisely what vertical, horizontal and diagonal mean.


Constructor & Destructor Documentation

regina::NSatLST::NSatLST ( const NSatLST cloneMe  ) 

Constructs a clone of the given block structure.

Parameters:
cloneMe the block structure to clone.
regina::NSatLST::~NSatLST (  ) 

Destroys this structure and its internal components.


Member Function Documentation

virtual void regina::NSatLST::adjustSFS ( NSFSpace sfs,
bool  reflect 
) const [virtual]

Adjusts the given Seifert fibred space to insert the contents of this saturated block.

In particular, the space should be adjusted as though an ordinary solid torus (base orbifold a disc, no twists or exceptional fibres) had been replaced by this block. This description does not make sense for blocks with twisted boundary; the twisted case is discussed below.

If the argument reflect is true, it should be assumed that this saturated block is being reflected before being inserted into the larger Seifert fibred space. That is, any twists or exceptional fibres should be negated before being added.

Regarding the signs of exceptional fibres: Consider a saturated block containing a solid torus whose meridinal curve runs p times horizontally around the boundary in order through annuli 0,1,... and follows the fibres q times from bottom to top (as depicted in the diagram in the NSatBlock class notes). Then this saturated block adds a positive (p, q) fibre to the underlying Seifert fibred space.

If the ring of saturated annuli bounding this block is twisted then the situation becomes more complex. It can be proven that such a block must contain a twisted reflector boundary in the base orbifold (use Z_2 homology with fibre-reversing paths to show that the base orbifold must contain another twisted boundary component, and then recall that real boundaries are not allowed inside blocks).

In this twisted boundary case, it should be assumed that the twisted reflector boundary is already stored in the given Seifert fibred space. This routine should make any further changes that are required (there may well be none). That is, the space should be adjusted as though a trivial Seifert fibred space over the annulus with one twisted reflector boundary (and one twisted puncture corresponding to the block boundary) had been replaced by this block. In particular, this routine should not add the reflector boundary itself.

Parameters:
sfs the Seifert fibred space to adjust.
reflect true if this block is to be reflected, or false if it should be inserted directly.

Implements regina::NSatBlock.

NSatBlock * regina::NSatLST::clone (  )  const [inline, virtual]

Returns a newly created clone of this saturated block structure.

A clone of the correct subclass of NSatBlock will be returned. For this reason, each subclass of NSatBlock must implement this routine.

Returns:
a new clone of this block.

Implements regina::NSatBlock.

static NSatLST* regina::NSatLST::isBlockLST ( const NSatAnnulus annulus,
TetList avoidTets 
) [static]

Determines whether the given annulus is a boundary annulus for a block of this type (layered solid torus).

This routine is a specific case of NSatBlock::isBlock(); see that routine for further details.

Parameters:
annulus the proposed boundary annulus that should form part of the new saturated block.
avoidTets the list of tetrahedra that should not be considered, and to which any new tetrahedra will be added.
Returns:
details of the saturated block if one was found, or null if none was found.
const NLayeredSolidTorus * regina::NSatLST::lst (  )  const [inline]

Returns details of the layered solid torus that this block represents.

Returns:
details of the layered solid torus.
NPerm regina::NSatLST::roles (  )  const [inline]

Describes how the layered solid torus is attached to the boundary annulus.

The NLayeredSolidTorus class notes describe top-level edge groups 0, 1 and 2 for a layered solid torus. On the other hand, the NSatAnnulus class notes define vertical, horizontal and diagonal edges on the boundary annulus.

Suppose that the permutation returned by this routine is r. This indicates that:

  • edge group r[0] is attached to the vertical annulus edges;
  • edge group r[1] is attached to the horizontal annulus edges;
  • edge group r[2] is attached to the diagonal annulus edges.

The image r[3] will always be 3.

Returns:
a description of how the layered solid torus is attached to the boundary annulus.
virtual void regina::NSatLST::transform ( const NTriangulation originalTri,
const NIsomorphism iso,
NTriangulation newTri 
) [virtual]

Adjusts the structure of this block according to the given isomorphism between triangulations.

Any triangulation-specific information will be transformed accordingly (for instance, the routine NSatAnnulus::transform() will be called for each boundary annulus).

Information regarding adjacent blocks will not be changed. Only structural information for this particular block will be updated.

The given isomorphism must describe a mapping from originalTri to newTri, and this block must currently refer to tetrahedra in originalTri. After this routine is called the block will instead refer to the corresponding tetrahedra in newTri (with changes in vertex/face numbering also accounted for).

Precondition:
This block currently refers to tetrahedra in originalTri, and iso describes a mapping from originalTri to newTri.
Warning:
Any subclasses of NSatBlock that store additional triangulation-specific information will need to override this routine. When doing so, be sure to call NSatBlock::transform() so that the generic changes defined here will still take place.
Parameters:
originalTri the triangulation currently used by this saturated block.
iso the mapping from originalTri to newTri.
newTri the triangulation to be used by the updated block structure.

Reimplemented from regina::NSatBlock.

virtual void regina::NSatLST::writeAbbr ( std::ostream &  out,
bool  tex = false 
) const [virtual]

Writes an abbreviated name or symbol for this block to the given output stream.

This name should reflect the particular block type, but need not provide thorough details.

The output should be no more than a handful of characters long, and no newline should be written. In TeX mode, no leading or trailing dollar signs should be written.

Python:
The parameter out does not exist; standard output will be used.
Parameters:
out the output stream to which to write.
tex true if the output should be formatted for TeX, or false if it should be in plain text format.

Implements regina::NSatBlock.

virtual void regina::NSatLST::writeTextShort ( std::ostream &  out  )  const [virtual]

Writes this object in short text format to the given output stream.

The output should fit on a single line and no newline should be written.

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

Implements regina::ShareableObject.


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).