Talk notes for Sep 2, 2014
October-14-14
3:50 PM
0:00:28 Every doodle has a canonical form.
0:02:30 A Brunnian doodle.
0:04:30 Goussarov is alternation in parameter space.
0:05:30 The "Borromean" alternation example.
0:07:10 The "linking number" - changes by one under a triple point move. This is the Arnold "strangeness".
0:08:10 "Positive" and "negative" triple points.
0:10:30 End of strangeness discussion.
0:11:00 n/n+1-discussion begins.
0:12:00 Always use a fixed rotation number.
0:12:40 Moving joint pieces.
0:14:25 What remains, including the "rotation number" integer.
0:15:35 Forgetting the "rotation" integers.
0:18:25 The "rotation" punchline.
0:20:00 Coming to "doodle links".
0:20:55 Smoothing the forks to get rotation-number-1 doodle links.
0:22:00 The subdivision/theta relation.
0:23:30 Result after moding by theta.
0:24:20 Anti-symmetry and proof.
0:26:00 The tetrahedron relation and proof.
0:32:20 The ring exchange relation.
0:32:50 Reducing to the "chords".
0:34:20 Removing monochromatic double points.
0:35:40 Cutting disks into small pieces.
0:36:30 Further cuttings near "shielded" double points.
0:38:15 Rushed end of cutting proof.
0:38:45 The combinatorial information in a "chord diagram".
0:39:20 PAUSE.