NAME

       dgt - Triangulate a 3-manifold or 4-manifold from a framed link

SYNOPSIS

       dgt { -3, --dim3 | -4, --dim4 } [ -g, --graph ] [ -r, --real ]

       dgt { -v, --version | -?, --help }

DESCRIPTION

       This utility builds a triangulation or coloured graph of a 3-manifold or 4-manifold from a framed link.

       For  3-manifolds,  the manifold constructed is the one obtained by performing integer Dehn surgery on the
       given link.

       For 4-manifolds, the manifold constructed is the one obtained by attaching 4-dimensional 2-handles to the
       4-ball along the framed link components.

       When you run DGT, it will ask you to input the underlying (unframed) link  at  the  console.   This  link
       should  be given in the format of a Planar Diagram (PD) code, specifically, in the same format as used by
       SnapPy. The simplest way to achieve this is to draw the link in SnapPy's PLink editor, and  copy  the  PD
       code generated by SnapPy via the InfoPD Code menu option in the editor.

              Warning: Do not include the PD: text preceding the code generated by the PLink editor in the input
              to  DGT.   Only  copy  and  input  the  code  itself,  which starts at the left square bracket and
              terminates with the right square bracket.

       For more information, see the full DGT manual, available from
        <URL:https://raburke.github.io/>.

OPTIONS

       -3, --dim3
              Build the 3-manifold obtained from integer Dehn surgery on the input link.

              One of --dim3 or --dim4 must be given as a command-line argument.

       -4, --dim4
              Build the 4-manifold obtained by attaching 2-handles along the components of the  framed  link  to
              the 4-ball.

              One of --dim3 or --dim4 must be given as a command-line argument.

       -g, --graph
              Output  an edge list of the edge-coloured graph associated to the manifold. Each node of the graph
              corresponds to a tetrahedron in the case of 3-manifolds  or  to  a  pentachoron  in  the  case  of
              4-manifolds.   Two  nodes  are  connected  by  a  c-coloured  edge  if  the two corresponding top-
              dimensional simplices of the triangulation have the facets  opposite  to  the  vertex  labelled  c
              identified.

       -r, --real
              For 4-manifolds, this option will build the triangulation with real boundary.

              By  default,  if  the manifold does not have boundary S3, it will be built with ideal boundary. If
              the manifold has boundary S3, then the resulting triangulation will be capped  off  to  produce  a
              closed manifold.

              This  option  will be ignored for 3-manifolds, as all 3-manifolds built from this construction are
              closed.

       -v, --version
              Show which version of Regina is being used, and exit immediately.

       -?, --help
              Display brief usage information, and exit immediately.

EXAMPLES

       The following builds the Poincare homology 3-sphere obtained by +1 surgery along the right handed trefoil
       knot.

           example$ dgt -3
           Enter PD Code of Diagram: [(6,4,1,3),(4,2,5,1),(2,6,3,5)]

           Writhe of
           Component 0: 3
           Enter integer framings for 2-handles (same order as in SnapPy's PLink Editor):
           1
           Self-framing component 0...
           Link should now be self-framed: writhe(component) = framing(component)...
           Writhe of
           Component 0: 1

           1     Generating Negative Curl of Type A (x,x,z,w)...
           2     Generating Negative Curl of Type A (x,x,z,w)...
           3     Generating Positive Crossing...
           4     Generating Positive Crossing...
           5     Generating Positive Crossing...

           Here is the isomorphism signature:
           GLvvQvPvALvzMAQAvAQQQPccgfekjpmswxtvywzrxyDABABCEDBCEFFFaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
           example$

       The following builds the complex projective plane by attaching a single 2-handle to the 4-ball along a +1
       framed unknot.

           example$ dgt -4
           Enter PD Code of Diagram: [(1,1,2,2)]

           Writhe of
           Component 0: 1
           Enter integer framings for 2-handles (same order as in SnapPy's PLink Editor):
           1
           Adding additional pair of cancelling curls to component 0 to guarantee existence of a quadricolour...
           Link should now be self-framed: writhe(component) = framing(component)...
           Writhe of
           Component 0: 1

           1     Generating Negative Curl of Type A (x,x,z,w)...
           2     Generating Positive Curl of Type A (x,y,y,w)...
           3     Generating Positive Curl of Type A (x,y,y,w)...

           Performing 1 quadricolour substitution...

           If manifold has (non-spherical) boundary, resulting triangulation will have ideal boundary.
           If manifold has spherical boundary, manifold will be capped off to produce a closed manifold.

           Here is the isomorphism signature:
           mLvAwAQAPQQcfffhijgjgjkkklklllaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
           example$

MACOS USERS

       If you downloaded a drag-and-drop app bundle, this utility is shipped inside it.  If you  dragged  Regina
       to the main Applications folder, you can run it as /Applications/Regina.app/Contents/MacOS/dgt.

WINDOWS USERS

       The  command-line  utilities  are  installed  beneath  the Program Files directory; on some machines this
       directory   is   called   Program   Files   (x86).    You   can   start   this   utility    by    running
       c:\Program Files\Regina\Regina 7.3.1\bin\dgt.exe.

AUTHOR

       This  utility  was written by Rhuaidi Burke <rhuaidi.burke@uq.edu.au>.  Many people have been involved in
       the development of Regina; see the users' handbook for a full list of credits.

                                                  14 March 2023                                           DGT(1)