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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 ngraphloop.h
* \brief Deals with graph manifolds formed from self-identified Seifert
* fibred spaces.
*/
#ifndef __NGRAPHLOOP_H
#ifndef __DOXYGEN
#define __NGRAPHLOOP_H
#endif
#include "manifold/nmanifold.h"
#include "utilities/nmatrix2.h"
namespace regina {
class NSFSpace;
/**
* \weakgroup manifold
* @{
*/
/**
* Represents a closed graph manifold formed by joining a
* single bounded Seifert fibred space to itself along a torus.
*
* The Seifert fibred space must have two boundary components, each a
* torus corresponding to a puncture in the base orbifold (with no
* fibre-reversing twist as one travels around the boundary).
*
* The way in which the two torus boundaries are joined together is specified
* by a 2-by-2 matrix \a M. This matrix relates the locations of the fibres
* and base orbifold on the two boundary tori.
*
* More specifically, suppose that \a f0 and \a o0 are generators of the
* first boundary torus, where \a f0 represents a directed fibre in the
* Seifert fibred space and \a o0 represents the oriented boundary of
* the base orbifold. Likewise, let \a f1 and \a o1 be generators of the
* second boundary torus representing a directed fibre and the oriented
* boundary of the base orbifold. Then the tori are joined together so
* that the curves \a f0, \a o0, \a f1 and \a o1 become related as follows:
*
* <pre>
* [f1] [f0]
* [ ] = M * [ ]
* [o1] [o0]
* </pre>
*
* See the page on \ref sfsnotation for details on some of the
* terminology used above.
*
* The optional NManifold routine getHomologyH1() is implemented, but
* the optional routine construct() is not.
*
* \todo \opt Speed up homology calculations involving orientable base
* spaces by adding rank afterwards, instead of adding generators for
* genus into the presentation matrix.
*/
class NGraphLoop : public NManifold {
private:
NSFSpace* sfs_;
/**< The bounded Seifert fibred space that is joined to itself. */
NMatrix2 matchingReln_;
/**< The matrix describing how the two boundary tori are joined;
see the class notes for details. */
public:
/**
* Creates a new graph manifold as a self-identified Seifert fibred
* space. The bounded Seifert fibred space and the four elements of
* the 2-by-2 matching matrix are all passed separately. The elements
* of the matching matrix combine to give the full matrix \a M as
* follows:
*
* <pre>
* [ mat00 mat01 ]
* M = [ ]
* [ mat10 mat11 ]
* </pre>
*
* Note that the new object will take ownership of the given
* Seifert fibred space, and when this object is destroyed the
* Seifert fibred space will be destroyed also.
*
* \pre The given Seifert fibred space has precisely two torus
* boundaries, corresponding to two untwisted punctures in the
* base orbifold.
* \pre The given matching matrix has determinant +1 or -1.
*
* @param sfs the bounded Seifert fibred space.
* @param mat00 the (0,0) element of the matching matrix.
* @param mat01 the (0,1) element of the matching matrix.
* @param mat10 the (1,0) element of the matching matrix.
* @param mat11 the (1,1) element of the matching matrix.
*/
NGraphLoop(NSFSpace* sfs, long mat00, long mat01,
long mat10, long mat11);
/**
* Creates a new graph manifold as a self-identified Seifert fibred
* space. The bounded Seifert fibred space and the entire 2-by-2
* matching matrix are each passed separately.
*
* Note that the new object will take ownership of the given
* Seifert fibred space, and when this object is destroyed the
* Seifert fibred space will be destroyed also.
*
* \pre The given Seifert fibred space has precisely two torus
* boundaries, corresponding to two punctures in the base orbifold.
* \pre The given matching matrix has determinant +1 or -1.
*
* @param sfs the bounded Seifert fibred space.
* @param matchingReln the 2-by-2 matching matrix.
*/
NGraphLoop(NSFSpace* sfs, const NMatrix2& matchingReln);
/**
* Destroys this structure along with the bounded Seifert
* fibred space and the matching matrix.
*/
~NGraphLoop();
/**
* Returns a reference to the bounded Seifert fibred space that
* is joined to itself.
*
* @return a reference to the bounded Seifert fibred space.
*/
const NSFSpace& sfs() const;
/**
* Returns a reference to the 2-by-2 matrix describing how the
* two boundary tori of the Seifert fibred space are joined together.
* See the class notes for details on precisely how this matrix is
* represented.
*
* @return a reference to the matching matrix.
*/
const NMatrix2& matchingReln() const;
/**
* Determines in a fairly ad-hoc fashion whether this
* representation of this space is "smaller" than the given
* representation of the given space.
*
* The ordering imposed on graph manifolds is purely aesthetic
* on the part of the author, and is subject to change in future
* versions of Regina. It also depends upon the particular
* representation, so that different representations of the same
* space may be ordered differently.
*
* All that this routine really offers is a well-defined way of
* ordering graph manifold representations.
*
* @param compare the representation with which this will be compared.
* @return \c true if and only if this is "smaller" than the
* given graph manifold representation.
*/
bool operator < (const NGraphLoop& compare) const;
NAbelianGroup* getHomologyH1() const;
std::ostream& writeName(std::ostream& out) const;
std::ostream& writeTeXName(std::ostream& out) const;
private:
/**
* Uses (1,1) twists, inversion and/or reflection to make the
* presentation of this space more aesthetically pleasing.
*/
void reduce();
/**
* Uses (1,1) twists and/or inversion to make the given matching
* matrix more aesthetically pleasing.
*
* This routine is for internal use by reduce().
*
* @param reln the matching matrix to simplify.
*/
static void reduce(NMatrix2& reln);
/**
* Uses (1,1) twists to make the given matching matrix more
* aesthetically pleasing.
*
* This routine is for internal use by reduce().
*
* @param reln the matching matrix to simplify.
*/
static void reduceBasis(NMatrix2& reln);
};
/*@}*/
// Inline functions for NGraphLoop
inline NGraphLoop::NGraphLoop(NSFSpace* sfs,
long mat00, long mat01, long mat10, long mat11) :
sfs_(sfs), matchingReln_(mat00, mat01, mat10, mat11) {
reduce();
}
inline NGraphLoop::NGraphLoop(NSFSpace* sfs, const NMatrix2& matchingReln) :
sfs_(sfs), matchingReln_(matchingReln) {
reduce();
}
inline const NSFSpace& NGraphLoop::sfs() const {
return *sfs_;
}
inline const NMatrix2& NGraphLoop::matchingReln() const {
return matchingReln_;
}
} // namespace regina
#endif
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