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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2011, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of the *
* License, or (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* General Public License for more details. *
* *
* You should have received a copy of the GNU General Public *
* License along with this program; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
/* end stub */
/*! \file subcomplex/npluggedtorusbundle.h
* \brief Supports self-identified Seifert fibred spaces that are
* triangulated using a combination of thin I-bundles and saturated blocks.
*/
#ifndef __NPLUGGEDTORUSBUNDLE_H
#ifndef __DOXYGEN
#define __NPLUGGEDTORUSBUNDLE_H
#endif
#include "regina-core.h"
#include "maths/nmatrix2.h"
#include "subcomplex/nstandardtri.h"
namespace regina {
class NIsomorphism;
class NSatRegion;
class NTxICore;
/**
* \weakgroup subcomplex
* @{
*/
/**
* Describes a triangulation of a graph manifold formed by joining a
* bounded saturated region with a thin I-bundle over the torus,
* possibly with layerings in between.
*
* The thin I-bundle must be untwisted, so that it forms the product
* <tt>T x I</tt> with two boundary tori. Moreover, it must be isomorphic
* to some existing instance of the class NTxICore.
*
* The saturated region is described by an object of the class NSatRegion.
* This region must have precisely two boundary annuli. These may be
* two separate torus boundaries (each formed from its own saturated annulus).
* Alternatively, the saturated region may have a single boundary formed
* from both saturated annuli, where this boundary is pinched together
* so that each annulus becomes its own two-sided torus.
*
* Either way, the saturated region effectively has two torus boundaries,
* each formed from two faces of the triangulation. These boundaries
* are then joined to the two torus boundaries of the thin I-bundle,
* possibly with layerings in between (for more detail on layerings, see
* the NLayering class). This is illustrated in the following diagram,
* where the small tunnels show where the torus boundaries are joined
* (possibly via layerings).
*
* <pre>
* /--------------------\ /-----------------\
* | ----- |
* | ----- |
* | Saturated region | | Thin I-bundle |
* | ----- |
* | ----- |
* \--------------------/ \-----------------/
* </pre>
*
* The effect of the thin I-bundle and the two layerings is essentially
* to join the two boundaries of the saturated region according to some
* non-trivial homeomorphism of the torus. This homeomorphism is
* specified by a 2-by-2 matrix \a M as follows.
*
* Suppose that \a f0 and \a o0 are directed curves on the first
* boundary torus and \a f1 and \a o1 are directed curves on the second
* boundary torus, where \a f0 and \a f1 represent the fibres of the
* saturated region and \a o0 and \a o1 represent the base orbifold (see
* the page on \ref sfsnotation for terminology).
* Then the torus boundaries of the saturated region are identified by
* the thin I-bundle and layerings according to the following relation:
*
* <pre>
* [f1] [f0]
* [ ] = M * [ ]
* [o1] [o0]
* </pre>
*
* Note that the routines writeName() and writeTeXName() do \e not offer
* enough information to uniquely identify the triangulation, since this
* essentially requires 2-dimensional assemblings of saturated blocks.
* For more detail, writeTextLong() may be used instead.
*
* The optional NStandardTriangulation routine getManifold() is
* implemented for this class, but getHomologyH1() is not.
*/
class REGINA_API NPluggedTorusBundle : public NStandardTriangulation {
private:
const NTxICore& bundle_;
/**< The thin I-bundle that appears within this triangulation.
This thin I-bundle is referenced from elsewhere (i.e., it
is not owned by this object), and its tetrahedra do not
belong to this triangulation (instead see the data member
\a bundleIso_). */
NIsomorphism* bundleIso_;
/**< A mapping from the thin I-bundle \a bundle_ to this
triangulation. This is required since the thin I-bundle
\a bundle_ is external, and does not refer directly to this
triangulation. */
NSatRegion* region_;
/**< The saturated region that appears within this
triangulation. This region is owned by this object, and
refers to tetrahedra within this triangulation. */
NMatrix2 matchingReln_;
/**< Describes how the two torus boundaries of the saturated
region are joined, as discussed in the class notes above. */
public:
/**
* Destroys this structure and its constituent components.
*
* As an exception, the thin I-bundle is not destroyed, since
* it is assumed that this is referenced from elsewhere.
*/
~NPluggedTorusBundle();
/**
* Returns an isomorphic copy of the thin I-bundle that forms part
* of this triangulation. Like all objects of class NTxICore, the
* thin I-bundle that is returned is an external object with its own
* separate triangulation of the product <tt>T x I</tt>. For
* information on how the thin I-bundle is embedded within this
* triangulation, see the routine bundleIso().
*
* @return the an isomorphic copy of the thin I-bundle within
* this triangulation.
*/
const NTxICore& bundle() const;
/**
* Returns an isomorphism describing how the thin I-bundle forms
* a subcomplex of this triangulation.
*
* The thin I-bundle returned by bundle() does not directly
* refer to tetrahedra within this triangulation. Instead it
* contains its own isomorphic copy of the thin I-bundle
* triangulation (as is usual for objects of class NTxICore).
*
* The isomorphism returned by this routine is a mapping from
* the triangulation bundle().core() to this triangulation,
* showing how the thin I-bundle appears as a subcomplex of this
* structure.
*
* @return an isomorphism from the thin I-bundle described
* by bundle() to the tetrahedra of this triangulation.
*/
const NIsomorphism& bundleIso() const;
/**
* Returns the saturated region that forms part of this triangulation.
* The region refers directly to tetrahedra within this triangulation
* (as opposed to the thin I-bundle, which refers to a separate
* external triangulation).
*
* @return the saturated region.
*/
const NSatRegion& region() const;
/**
* Returns the matrix describing how the two torus boundaries of
* the saturated region are joined by the thin I-bundle and
* layerings. See the class notes above for details.
*
* @return the matching relation between the two region boundaries.
*/
const NMatrix2& matchingReln() const;
NManifold* getManifold() const;
std::ostream& writeName(std::ostream& out) const;
std::ostream& writeTeXName(std::ostream& out) const;
void writeTextLong(std::ostream& out) const;
/**
* Determines if the given triangulation is a saturated region
* joined to a thin I-bundle via optional layerings, as described
* in the class notes above.
*
* @param tri the triangulation to examine.
* @return a newly created object containing details of the
* structure that was found, or \c null if the given
* triangulation is not of the form described by this class.
*/
static NPluggedTorusBundle* isPluggedTorusBundle
(NTriangulation* tri);
private:
/**
* Creates a new structure of the form described in the class notes
* above, based on the given constituent components. The new object
* will take ownership of the given saturated region and isomorphism.
* It will not take ownership of the given thin I-bundle.
*
* Note that the new object must refer to an existing triangulation.
*
* \warning The thin I-bundle \a bundle must have a lifetime at
* least as long as the new object being created, since it will
* be referenced directly by this new object.
*
* @param bundle the thin I-bundle whose isomorphic copy is used
* within the triangulation described by the new object.
* @param bundleIso the corresponding isomorphism from the given
* thin I-bundle to the triangulation described by the new object.
* @param region the saturated region used within the new object.
* @param matchingReln the matching relation describing how the
* two saturated region boundaries are joined by the thin
* I-bundle and layerings, as described in the class notes above.
*/
NPluggedTorusBundle(const NTxICore& bundle, NIsomorphism* bundleIso,
NSatRegion* region, const NMatrix2& matchingReln);
/**
* Determines whether the given triangulation is of the form
* described by this class, with the constraint that the
* thin I-bundle used within the triangulation must be isomorphic
* to the given thin I-bundle.
*
* This routine is internal to isPluggedTorusBundle().
*
* \pre The given triangulation is closed and connected.
*
* \warning If this routine is successful and a new object is
* returned, this new object must not outlive the given thin
* I-bundle (since the new object will in fact contain a direct
* reference to this thin I-bundle).
*
* @param tri the triangulation to examine.
* @param bundle the thin I-bundle whose isomorphic copy must be
* used in the given triangulation.
* @return a newly created object containing details of the
* structure that was found, or \c null if the given triangulation
* is not of the form described by this class using an isomorphic
* copy of the given thin I-bundle.
*/
static NPluggedTorusBundle* hunt(NTriangulation* tri,
const NTxICore& bundle);
};
/*@}*/
// Inline functions for NPluggedTorusBundle
inline NPluggedTorusBundle::NPluggedTorusBundle(const NTxICore& bundle,
NIsomorphism* bundleIso, NSatRegion* region,
const NMatrix2& matchingReln) :
bundle_(bundle), bundleIso_(bundleIso), region_(region),
matchingReln_(matchingReln) {
}
inline const NTxICore& NPluggedTorusBundle::bundle() const {
return bundle_;
}
inline const NIsomorphism& NPluggedTorusBundle::bundleIso() const {
return *bundleIso_;
}
inline const NSatRegion& NPluggedTorusBundle::region() const {
return *region_;
}
inline const NMatrix2& NPluggedTorusBundle::matchingReln() const {
return matchingReln_;
}
} // namespace regina
#endif
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