KATIE(1)                      The Regina Handbook                     KATIE(1)



NAME
       katie - Triangulate a 3-manifold or 4-manifold from a decorated link

SYNOPSIS
       katie pd_code framing_vector [ -3, --dim3 | -4, --dim4 ] [ -g, --graph
       ] [ -V, --verbose ]


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


DESCRIPTION
       This utility builds a triangulation or coloured graph of a 3-manifold
       or 4-manifold from a decorated 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 1- and 2-handles to the 4-ball along the dotted
       and framed link components, respectively.

       Katie expects two arguments at runtime: the underlying (undecorated)
       link, and a list of space-separated decorations (framing coefficients
       and/or 1-handle "markers").

       o The 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.

       o Within the framing sequence, use 'x' or '.' to denote 1-handles.

         Warning: The PD code and the framing sequence must appear as the
         first two arguments.  If you are running Katie from a shell, you will
         need to wrap both of these arguments in quotation marks.

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

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

              If you do not pass either --dim3 or --dim4, the default is to
              build a 4-manifold.

       -4, --dim4
              Build the 4-manifold obtained by attaching 1- and 2-handles
              along the components of the decorated link to the 4-ball.

              This option is the default if you do not pass either --dim3 or
              --dim4.

       -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.

       -V, --verbose
              Display information during the construction.

       -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$ katie "[(6,4,1,3),(4,2,5,1),(2,6,3,5)]" "1" -3
           Writhes:
           Component 0: 2-handle, writhe 1

           Here is the isomorphism signature:
           GLvvQvPvALvzMAQAvAQQQPccgfekjp...
           example$

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

           example$ katie "[(1,1,2,2)]" "1"
           Writhes:
           Component 0: 2-handle, writhe 1

           Here is the isomorphism signature:
           mLvAwAQAPQQcfffhijgjgjkkklklll...
           example$

       The following builds a 4-manifold containing both a 1- and a 2-handle.

           example$ katie "[(4,8,1,9),(9,3,10,4),(1,5,2,6),(6,2,7,3),(7,5,8,10)]" "x 0"
           Writhes:
           Component 0: 1-handle (0)
           Component 1: 2-handle, writhe 0

           Here is the isomorphism signature:
           SLvAvAAwvvALMQQPvPvPMQwQAQMAvQ...
           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/katie.

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 7.4.1\bin\katie.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.

                                25 August 2025                        KATIE(1)