Notes for AKT-090910-1/0:29:24: Difference between revisions
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<u>Terminology</u> (for the purpose of this annotation)<br> |
<u>Terminology</u> (for the purpose of this annotation)<br> |
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<b>Local rule</b>: at each crossing, of the 3 arcs involved, either 1 or all 3 colours appear.<br> |
<b>Local rule</b>: at each crossing, of the 3 arcs involved, either 1 or all 3 colours appear.<br> |
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<b>Global rule</b>: all |
<b>Global rule</b>: all 3 colours must appear.<br> |
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(Together with the provision of 3 colours, knots which can be coloured obeying these rules, are called <b>tricolourable</b> as defined at 0:10:26 of this hour.) |
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Latest revision as of 16:25, 22 September 2009
Invariance of tricolourability under R2. For each of the 2 directions (as in the proof for R1), there are cases (corresponding to different colourings of, say the top, 'external endpoints' of the local diagram modulo colour permutations; the colouring of all arcs will then be forced by the local rule of tricolourability and the fact that we are only dealing with three colours, and the cases which violate the global rule should be discarded) to check.
Terminology (for the purpose of this annotation)
Local rule: at each crossing, of the 3 arcs involved, either 1 or all 3 colours appear.
Global rule: all 3 colours must appear.
(Together with the provision of 3 colours, knots which can be coloured obeying these rules, are called tricolourable as defined at 0:10:26 of this hour.)
