connections

Description

A connections element encodes the connections between the different crossings in a knot/link diagram. Recall that knot/link diagrams in Regina are oriented, and the crossings in a diagram are numbered 0, 1, 2, and so on.

If a link diagram has n crossings, then the character data of this XML element should be a whitespace-separated list of exactly 2n tokens. These represent the connections from the upper strand of crossing 0, then the lower strand of crossing 0, then the upper strand of crossing 1, then the lower strand of crossing 1, and so on. By “the connection from” some strand of some crossing, we mean the next crossing that you encounter if you traverse the (oriented) link from the original strand/crossing.

Each such token encodes either the upper or lower strand of some crossing. It should be in the form ^k to encode the upper strand of crossing number k, or the form _k to encode the lower strand of crossing number k. Here the symbols ^ and _ are literal characters, whereas k should be replaced by a crossing number.

Example

The following XML snippet represents the Whitehead link.

<crossings size="5">
- - + + -
</crossings>
<connections>
_1 ^1
_2 ^4
_4 ^3
_0 ^2
_3 ^0
</connections>
<components size="2">
^0 _0
</components>