Regina Calculation Engine
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Offers routines for constructing a variety of sample 4-dimensional triangulations. More...
#include <triangulation/example4.h>
Static Public Member Functions | |
static Triangulation< dim > * | sphere () |
Closed Triangulations. More... | |
static Triangulation< dim > * | simplicialSphere () |
Returns the standard (dim+2)-simplex triangulation of the dim-sphere as the boundary of a (dim+1)-simplex. More... | |
static Triangulation< dim > * | sphereBundle () |
Returns a two-simplex triangulation of the product space S^(dim-1) x S^1 . More... | |
static Triangulation< dim > * | twistedSphereBundle () |
Returns a two-simplex triangulation of the twisted product space S^(dim-1) x~ S^1 . More... | |
static Triangulation< dim > * | ball () |
Bounded Triangulations. More... | |
static Triangulation< dim > * | ballBundle () |
Returns a triangulation of the product space B^(dim-1) x S^1 . More... | |
static Triangulation< dim > * | twistedBallBundle () |
Returns a triangulation of the twisted product space B^(dim-1) x~ S^1 . More... | |
Closed Triangulations | |
static Triangulation< 4 > * | fourSphere () |
Returns a two-pentachoron triangulation of the 4-sphere. More... | |
static Triangulation< 4 > * | simplicialFourSphere () |
Returns the standard six-pentachoron triangulation of the 4-sphere as the boundary of a 5-simplex. More... | |
static Triangulation< 4 > * | rp4 () |
Returns a four-pentachoron triangulation of real projective 4-space. More... | |
static Triangulation< 4 > * | s3xs1 () |
Returns a two-pentachoron triangulation of the product space S^3 x S^1 . More... | |
static Triangulation< 4 > * | s3xs1Twisted () |
Returns a two-pentachoron triangulation of the twisted product space S^3 x~ S^1 . More... | |
Ideal Triangulations | |
(end: Closed Triangulations) | |
static Triangulation< 4 > * | cappellShaneson () |
Returns a two-pentachoron triangulation of a Cappell-Shaneson 2-knot complement in the 4-sphere. More... | |
Constructions from 3-Manifold Triangulations | |
(end: Ideal Triangulations) | |
static Triangulation< 4 > * | iBundle (const Triangulation< 3 > &base) |
Returns a triangulation of the product M x I , where M is the given 3-manifold triangulation. More... | |
static Triangulation< 4 > * | s1Bundle (const Triangulation< 3 > &base) |
Returns a triangulation of the product M x S1 , where M is the given 3-manifold triangulation. More... | |
static Triangulation< 4 > * | bundleWithMonodromy (const Triangulation< 3 > &base, const Isomorphism< 3 > &monodromy) |
Returns a bundle formed from a given 3-manifold and a given monodromy. More... | |
Offers routines for constructing a variety of sample 4-dimensional triangulations.
This is a specialisation of the generic Example class template; see the Example template documentation for a general overview of how the example triangulation classes work.
This 4-dimensional specialisation offers significant extra functionality, by providing several more hard-coded and parameterised constructions.
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staticinherited |
Bounded Triangulations.
Returns a one-simplex triangulation of the dim-ball.
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staticinherited |
Returns a triangulation of the product space B^(dim-1) x S^1
.
This will use one simplex in odd dimensions, or two simplices in even dimensions.
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staticinherited |
Returns the standard (dim+2)-simplex triangulation of the dim-sphere as the boundary of a (dim+1)-simplex.
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staticinherited |
Closed Triangulations.
Returns a two-simplex triangulation of the dim-sphere.
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staticinherited |
Returns a two-simplex triangulation of the product space S^(dim-1) x S^1
.
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staticinherited |
Returns a triangulation of the twisted product space B^(dim-1) x~ S^1
.
This will use one simplex in even dimensions, or two simplices in odd dimensions.
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staticinherited |
Returns a two-simplex triangulation of the twisted product space S^(dim-1) x~ S^1
.