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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 manifold/notation.h
* \brief Explains notation used for describing various types of 3-manifold.
*/
/*! \page sfsnotation Notation for Seifert fibred spaces
*
* Consider a Seifert fibred space over some base orbifold, containing
* one or more exceptional fibres and optionally one or more boundary
* components. Here we describe the notation used for the exceptional
* fibres, as well as their relationship to curves on the boundary
* components.
*
* Consider the illustration below. Here the base orbifold is
* an annulus, with boundary components at the top and bottom of the
* diagram. The two circles in the middle correspond to two
* exceptional fibres.
*
* \image html sfsnotation.png
*
* The boundary curves \a o1 and \a o2, as well as the curves \a e1 and
* \a e2 bounding the exceptional fibres, can be given consistent
* orientations as illustrated by the arrows. The fibres can also be
* consistently oriented; let them be parallel copies of some curve \a f.
*
* Suppose that we describe the space as having exceptional fibres
* with parameters (\a p1, \a q1) and (\a p2, \a q2). This corresponds
* to removing all fibres inside curves \a e1 and \a e2, and filling
* the resulting boundaries with solid tori whose meridinal curves are
* (\a p1 * \a e1 + \a q1 * \a f) and (\a p2 * \a e2 + \a q2 * \a f).
*
* An obstruction constant of \a b is treated as an additional
* exceptional fibre with parameters (1, \a b) according to the
* description above.
*
* Where necessary, we use the oriented curves \a o1 and \a o2 as
* curves on the boundaries <i>"representing the base orbifold"</i>,
* and parallel copies of \a f as curves on the boundaries
* <i>"representing the fibres"</i>. This becomes particularly
* important when joining different boundary components together.
*
* It is worth noting the following observation. Suppose we have a
* Seifert fibred space with boundary, and let one of its
* boundary components have oriented curves (\a f, \a o) representing the
* fibres and base orbifold respectively. Then exactly the same space can
* be written with an additional (1,1) fibre (i.e., the obstruction
* constant \a b is incremented by one), with the effect that the
* curves on that boundary representing the fibres and base orbifold
* become (\a f, \a o + \a f) instead.
*/
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