Regina Calculation Engine
Static Public Member Functions | List of all members
regina::Example< 4 > Class Reference

Offers routines for constructing a variety of sample 4-dimensional triangulations. More...

#include <triangulation/example4.h>

Inheritance diagram for regina::Example< 4 >:
regina::detail::ExampleBase< 4 >

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...
 

Detailed Description

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.

Member Function Documentation

◆ ball()

Triangulation< dim > * regina::detail::ExampleBase< dim >::ball
staticinherited

Bounded Triangulations.

Returns a one-simplex triangulation of the dim-ball.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ ballBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::ballBundle
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.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ simplicialSphere()

Triangulation< dim > * regina::detail::ExampleBase< dim >::simplicialSphere
staticinherited

Returns the standard (dim+2)-simplex triangulation of the dim-sphere as the boundary of a (dim+1)-simplex.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ sphere()

Triangulation< dim > * regina::detail::ExampleBase< dim >::sphere
staticinherited

Closed Triangulations.

Returns a two-simplex triangulation of the dim-sphere.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ sphereBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::sphereBundle
staticinherited

Returns a two-simplex triangulation of the product space S^(dim-1) x S^1.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ twistedBallBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::twistedBallBundle
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.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

◆ twistedSphereBundle()

Triangulation< dim > * regina::detail::ExampleBase< dim >::twistedSphereBundle
staticinherited

Returns a two-simplex triangulation of the twisted product space S^(dim-1) x~ S^1.

Returns
a newly constructed triangulation, which must be destroyed by the caller of this routine.

The documentation for this class was generated from the following file:

Copyright © 1999-2021, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).