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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2025, 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. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* 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, see <https://www.gnu.org/licenses/>. *
* *
**************************************************************************/
#include "algebra/abeliangroup.h"
#include "manifold/sfs.h"
#include "maths/matrix.h"
#include "subcomplex/layeredchainpair.h"
#include "triangulation/dim3.h"
namespace regina {
std::unique_ptr<LayeredChainPair> LayeredChainPair::recognise(
const Component<3>* comp) {
// Basic property check.
if ((! comp->isClosed()) || (! comp->isOrientable()))
return nullptr;
size_t nTet = comp->size();
if (nTet < 2)
return nullptr;
if (comp->countVertices() != 1)
return nullptr;
// We have at least two tetrahedra and precisely 1 vertex.
// The component is closed and orientable (and connected, since it's
// a component).
// Start with tetrahedron 0. This must belong to *some* chain.
Tetrahedron<3>* base = comp->tetrahedron(0);
// Note that we only need check permutations in S3 since we can
// arbitrarily assign the role of one vertex in the tetrahedron.
for (auto p3: Perm<3>::S3) {
LayeredChain first(base, Perm<4>::extend(p3));
first.extendMaximal();
Tetrahedron<3>* firstTop = first.top();
Tetrahedron<3>* firstBottom = first.bottom();
Perm<4> firstTopRoles = first.topVertexRoles();
Perm<4> firstBottomRoles = first.bottomVertexRoles();
// Check to see if the first chain fills the entire component.
if (first.index() == nTet) {
// The only success here will be if we have a chain pair of
// indices (n-1) and 1, which is in fact a layered loop.
LayeredChain longChain(firstBottom, firstBottomRoles);
if (longChain.extendBelow())
if (longChain.bottom() == firstTop &&
longChain.bottomVertexRoles() ==
firstTopRoles * Perm<4>(3, 2, 1, 0)) {
// We've got a layered loop!
if (nTet == 2) {
// The new chain is already too long.
longChain = LayeredChain(firstBottom, firstBottomRoles);
}
// Extend longChain to (n-1) tetrahedra.
while (longChain.index() + 1 < nTet)
longChain.extendBelow();
return std::unique_ptr<LayeredChainPair>(
new LayeredChainPair(
LayeredChain(
firstBottom->adjacentTetrahedron(
firstBottomRoles[0]),
firstBottom->adjacentGluing(
firstBottomRoles[0]) * firstBottomRoles *
Perm<4>(0, 2, 1, 3)),
longChain));
}
continue;
}
// At this point we must have run into the second chain.
Tetrahedron<3>* secondBottom = firstTop->adjacentTetrahedron(
firstTopRoles[3]);
if (secondBottom == firstTop || secondBottom == firstBottom ||
! secondBottom) {
continue;
}
LayeredChain second(secondBottom,
firstTop->adjacentGluing(firstTopRoles[3]) *
firstTopRoles * Perm<4>(1, 3, 0, 2));
while (second.extendAbove())
;
if (second.index() + first.index() != nTet)
continue;
Tetrahedron<3>* secondTop = second.top();
Perm<4> secondTopRoles = second.topVertexRoles();
Perm<4> secondBottomRoles = second.bottomVertexRoles();
// At this point we have two chains that together have the
// correct number of tetrahedra. All we need do is check the
// remaining three between-chain gluings.
if (secondTop == firstTop->adjacentTetrahedron(firstTopRoles[0]) &&
secondBottom == firstBottom->adjacentTetrahedron(
firstBottomRoles[2]) &&
secondTop == firstBottom->adjacentTetrahedron(
firstBottomRoles[1]) &&
secondTopRoles == firstTop->adjacentGluing(
firstTopRoles[0]) * firstTopRoles * Perm<4>(0, 2, 1, 3) &&
secondBottomRoles == firstBottom->adjacentGluing(
firstBottomRoles[2]) * firstBottomRoles *
Perm<4>(3, 1, 2, 0) &&
secondTopRoles == firstBottom->adjacentGluing(
firstBottomRoles[1]) * firstBottomRoles *
Perm<4>(2, 0, 3, 1)) {
// We found one!
if (first.index() > second.index())
return std::unique_ptr<LayeredChainPair>(
new LayeredChainPair(second, first));
else
return std::unique_ptr<LayeredChainPair>(
new LayeredChainPair(first, second));
}
}
// Nothing was found. Sigh.
return nullptr;
}
std::unique_ptr<Manifold> LayeredChainPair::manifold() const {
std::unique_ptr<SFSpace> ans(new SFSpace());
ans->insertFibre(2, -1);
ans->insertFibre(chain_[0].index() + 1, 1);
ans->insertFibre(chain_[1].index() + 1, 1);
ans->reduce();
return ans;
}
AbelianGroup LayeredChainPair::homology() const {
// The first homology group can be obtained from the matrix:
//
// [ 1 -1 1 ]
// [ n_1 1 1 ]
// [ 1 n_2 -1 ]
//
// This is established simply by examining the edges on the boundary
// of each layered chain.
MatrixInt mat(3, 3);
mat.fill(1);
mat.entry(0, 1) = mat.entry(2, 2) = -1;
mat.entry(1, 0) = chain_[0].index();
mat.entry(2, 1) = chain_[1].index();
return AbelianGroup(std::move(mat));
}
} // namespace regina
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