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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2008, 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 nblockedsfsloop.h
* \brief Supports self-identified Seifert fibred spaces that are
* triangulated using saturated blocks.
*/
#ifndef __NBLOCKEDSFSLOOP_H
#ifndef __DOXYGEN
#define __NBLOCKEDSFSLOOP_H
#endif
#include "subcomplex/nstandardtri.h"
#include "utilities/nmatrix2.h"
namespace regina {
class NSatRegion;
/**
* \weakgroup subcomplex
* @{
*/
/**
* Represents a blocked Seifert fibred space with two boundary tori that
* are joined together. This is a particular type of triangulation of a
* graph manifold, formed from a single saturated region whose two torus
* boundaries are identified. An optional layering may be placed
* between the two torus boundaries to allow for a more interesting
* relationship between the two sets of boundary curves. For more
* detail on saturated regions and their constituent saturated blocks,
* see the NSatRegion class; for more detail on layerings, see the
* NLayering class.
*
* The saturated region may have two boundary components formed from one
* saturated annulus each. Alternatively, it may have one boundary
* formed from two saturated annuli, where this boundary is pinched
* together so that each annulus becomes a two-sided torus (both of which
* are later joined together). None of the boundary components (or the
* two-sided tori discussed above) may be twisted (i.e., they must be
* tori, not Klein bottles).
*
* The way in which the two torus boundaries are identified is specified
* by a 2-by-2 matrix, which expresses curves representing the fibres
* and base orbifold on the second boundary in terms of such curves on
* the first boundary (see the page on \ref sfsnotation for terminology).
*
* More specifically, 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 region and \a o0 and \a o1 represent the base orbifold.
* Then the boundaries are joined according to the following relation:
*
* <pre>
* [f1] [f0]
* [ ] = M * [ ]
* [o1] [o0]
* </pre>
*
* If a layering is present between the two torus boundaries, then the
* corresponding boundary curves are not identified directly. In this
* case, the matrix \a M shows how the layering relates the curves on
* each boundary.
*
* 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 full details, writeTextLong() may be used instead.
*
* The optional NStandardTriangulation routine getManifold() is
* implemented for this class, but getHomologyH1() is not.
*/
class NBlockedSFSLoop : public NStandardTriangulation {
private:
NSatRegion* region_;
/**< The saturated region whose two torus boundaries are joined. */
NMatrix2 matchingReln_;
/**< Specifies how the two boundary tori are joined, as described
in the class notes above. */
public:
/**
* Destroys this structure and its constituent components.
*/
~NBlockedSFSLoop();
/**
* Returns details of the saturated region from which this
* triangulation is formed. See the class notes above for
* further information.
*
* @return details of the saturated region.
*/
const NSatRegion& region() const;
/**
* Returns the matrix describing how the two torus boundaries of
* the saturated region are joined. Note that if a layering is
* placed between the two boundary tori, then any changes to the
* boundary relationships caused by the layering are included in
* this matrix.
*
* See the class notes above for precise information on how this
* matrix is presented.
*
* @return the matrix describing how the boundaries of the
* region are joined.
*/
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 blocked Seifert
* fibred space with identified boundaries, as described by this
* class.
*
* @param tri the triangulation to examine.
* @return a newly created structure containing details of the
* blocked self-identified Seifert fibred space, or \c null if
* the given triangulation is not of this form.
*/
static NBlockedSFSLoop* isBlockedSFSLoop(NTriangulation* tri);
private:
/**
* Constructs a new blocked self-identified Seifert fibred
* space, as described by the given saturated region and
* matching relation. The new object will take ownership of the
* given region.
*
* Note that the new object must describe an existing triangulation.
*
* @param region the saturated region from which the structure
* is formed.
* @param matchingReln describes how the two boundaries of the
* region are joined, as described in the class notes above.
*/
NBlockedSFSLoop(NSatRegion* region, const NMatrix2& matchingReln);
};
/*@}*/
// Inline functions for NBlockedSFSLoop
inline NBlockedSFSLoop::NBlockedSFSLoop(NSatRegion* region,
const NMatrix2& matchingReln) :
region_(region), matchingReln_(matchingReln) {
}
inline const NSatRegion& NBlockedSFSLoop::region() const {
return *region_;
}
inline const NMatrix2& NBlockedSFSLoop::matchingReln() const {
return matchingReln_;
}
} // namespace regina
#endif
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