---
name: "katie"
section: "1"
platform: "linux"
package: "regina"
version: "7.4.1-4"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/katie"
---

# katie(1)

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

## 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").

- •

  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.

- •

  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.