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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/lensspace.h"
#include "manifold/sfs.h"
#include "subcomplex/layeredloop.h"
#include "triangulation/dim3.h"
namespace regina {
std::unique_ptr<Manifold> LayeredLoop::manifold() const {
if (hinge_[1]) {
// Not twisted.
return std::make_unique<LensSpace>(length_, 1);
} else {
// Twisted.
std::unique_ptr<SFSpace> ans(new SFSpace());
ans->insertFibre(2, -1);
ans->insertFibre(2, 1);
ans->insertFibre(length_, 1);
ans->reduce();
return ans;
}
}
std::unique_ptr<LayeredLoop> LayeredLoop::recognise(const Component<3>* comp) {
// Basic property check.
if ((! comp->isClosed()) || (! comp->isOrientable()))
return nullptr;
size_t nTet = comp->size();
if (nTet == 0)
return nullptr;
size_t nVertices = comp->countVertices();
if (nVertices > 2)
return nullptr;
bool twisted = (nVertices == 1);
// We have at least 1 tetrahedron and precisely 1 or 2 vertices.
// The component is closed and orientable (and connected, since it's
// a component).
// Pick our base tetrahedron.
Tetrahedron<3>* base = comp->tetrahedron(0);
Tetrahedron<3>* tet = base;
int adjTop0 = 0, adjTop1 = 0, adjBottom0 = 0, adjBottom1 = 0;
// Declare 0 to be a top face; find its partner.
int baseTop0 = 0;
Tetrahedron<3>* next = base->adjacentTetrahedron(0);
for (int baseTop1 = 1; baseTop1 < 4; baseTop1++) {
if (base->adjacentTetrahedron(baseTop1) != next)
continue;
// Find the vertex joined to baseTop0 by a hinge.
for (int baseBottom0 = 1; baseBottom0 < 4; baseBottom0++) {
if (baseBottom0 == baseTop1)
continue;
int baseBottom1 = 6 - baseBottom0 - baseTop0 - baseTop1;
// Some basic property checks.
if (base->adjacentTetrahedron(baseBottom0) !=
base->adjacentTetrahedron(baseBottom1))
continue;
int hinge0 = Edge<3>::edgeNumber[baseTop0][baseBottom0];
int hinge1 = Edge<3>::edgeNumber[baseTop1][baseBottom1];
if (twisted) {
if (base->edge(hinge0) != base->edge(hinge1))
continue;
if (base->edge(hinge0)->degree() != 2 * nTet)
continue;
} else {
if (base->edge(hinge0)->degree() != nTet)
continue;
if (base->edge(hinge1)->degree() != nTet)
continue;
}
int top0 = baseTop0;
int top1 = baseTop1;
int bottom0 = baseBottom0;
int bottom1 = baseBottom1;
// Follow the gluings up.
bool ok = true;
while (true) {
// Already set: tet, next, topi, bottomi.
// Check that both steps up lead to the same tetrahedron.
// Note that this check has already been done for the first
// iteration of this loop; never mind, no big loss.
if (tet->adjacentTetrahedron(top0) !=
tet->adjacentTetrahedron(top1)) {
ok = false;
break;
}
// Check that the corresponding gluings are correct.
Perm<4> p = tet->adjacentGluing(top0);
adjTop0 = p[bottom0];
adjTop1 = p[top1];
adjBottom0 = p[top0];
adjBottom1 = p[bottom1];
p = tet->adjacentGluing(top1);
// Note that only three of the four comparisons are needed.
if (adjTop0 != p[top0] || adjTop1 != p[bottom1] ||
adjBottom0 != p[bottom0]) {
ok = false;
break;
}
// If we've finished the loop, exit at this point so we
// can check that it all glued up correctly.
if (next == base)
break;
// We haven't finished the loop, so the next
// tetrahedron should be different from this one.
if (next == tet) {
ok = false;
break;
}
// Move to the next tetrahedron.
top0 = adjTop0; top1 = adjTop1;
bottom0 = adjBottom0; bottom1 = adjBottom1;
tet = next;
next = tet->adjacentTetrahedron(top0);
}
if (ok) {
// Make sure the final gluing wraps everything up
// correctly.
if (twisted) {
if (adjTop0 != baseTop1 || adjTop1 != baseTop0 ||
adjBottom0 != baseBottom1)
continue;
} else {
if (adjTop0 != baseTop0 || adjTop1 != baseTop1 ||
adjBottom0 != baseBottom0)
continue;
}
// We have a solution!
return std::unique_ptr<LayeredLoop>(new LayeredLoop(
nTet, base->edge(hinge0),
(twisted ? nullptr : base->edge(hinge1))));
}
}
}
// Nothing found.
return nullptr;
}
AbelianGroup LayeredLoop::homology() const {
if (hinge_[1]) {
// Untwisted.
if (length_ > 1)
return AbelianGroup(0, {length_});
else
return AbelianGroup();
} else {
// Twisted.
if (length_ % 2 == 0)
return AbelianGroup(0, {2,2});
else
return AbelianGroup(0, {4});
}
}
} // namespace regina
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