Meta-Groups, Meta-Bicrossed-Products, and the Alexander Polynomial
Seminar Room 1, Newton Institute
AbstractI will define "meta-groups" and explain how one specific meta-group, which in itself is a "meta-bicrossed-product", gives rise to an "ultimate Alexander invariant" of tangles, that contains the Alexander polynomial (multivariable, if you wish), has extremely good composition properties, is evaluated in a topologically meaningful way, and is least-wasteful in a computational sense. If you believe in categorification, that's a wonderful playground.
This will be a repeat of a talk I gave in Regina in August 2012 and in a number of other places, and I plan to repeat it a good further number of places. Though here at the Newton Institute I plan to make the talk a bit longer, giving me more time to give some further fun examples of meta-structures, and perhaps I will learn from the audience that these meta-structures should really be called something else. The slides of the talk are availble here: http://www.math.toronto.edu/~drorbn/Talks/Newton-1301/#Talk2.