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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2009, 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 */
#include "algebra/nabeliangroup.h"
#include "manifold/nlensspace.h"
#include "triangulation/ncomponent.h"
#include "triangulation/ntetrahedron.h"
#include "triangulation/nvertex.h"
#include "subcomplex/nl31pillow.h"
namespace regina {
NL31Pillow* NL31Pillow::clone() const {
NL31Pillow* ans = new NL31Pillow();
ans->tet[0] = tet[0];
ans->tet[1] = tet[1];
ans->interior[0] = interior[0];
ans->interior[1] = interior[1];
return ans;
}
NL31Pillow* NL31Pillow::isL31Pillow(const NComponent* comp) {
// Basic property check.
if (comp->getNumberOfTetrahedra() != 2 ||
comp->getNumberOfVertices() != 2 ||
comp->getNumberOfEdges() != 4 ||
(! comp->isClosed()) ||
(! comp->isOrientable()))
return 0;
// Verify that the vertices have degrees 2 and 6.
int internalVertex;
unsigned long deg0 = comp->getVertex(0)->getNumberOfEmbeddings();
if (deg0 == 2)
internalVertex = 0;
else if (deg0 == 6)
internalVertex = 1;
else
return 0;
// Verify that all four faces of one tetrahedron join to the other.
NTetrahedron* tet[2];
tet[0] = comp->getTetrahedron(0);
tet[1] = comp->getTetrahedron(1);
if (tet[0]->adjacentTetrahedron(0) != tet[1] ||
tet[0]->adjacentTetrahedron(1) != tet[1] ||
tet[0]->adjacentTetrahedron(2) != tet[1] ||
tet[0]->adjacentTetrahedron(3) != tet[1])
return 0;
// At this point we can prove through enumeration of all
// 2-tetrahedron triangulations that we have our triangular pillow
// L(3,1).
NL31Pillow* ans = new NL31Pillow();
ans->tet[0] = tet[0];
ans->tet[1] = tet[1];
for (int i = 0; i < 2; i++) {
const NVertexEmbedding& emb = comp->getVertex(internalVertex)->
getEmbedding(i);
if (emb.getTetrahedron() == tet[0])
ans->interior[0] = emb.getVertex();
else
ans->interior[1] = emb.getVertex();
}
return ans;
}
NManifold* NL31Pillow::getManifold() const {
return new NLensSpace(3, 1);
}
NAbelianGroup* NL31Pillow::getHomologyH1() const {
NAbelianGroup* ans = new NAbelianGroup();
ans->addTorsionElement(3);
return ans;
}
} // namespace regina
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