NAME

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

SYNOPSIS

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

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.

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 7.1\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.

                                        11 September 2022                                  DGT(1)