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Ring Around the Rosie Midsummer Sunrise on Stonehenge The Hour Glass

From Stonehenge to Drinfel'd skipping all the details

Southern California Topology Colloquium, UC Riverside, April 29, 2000

Dror Bar-Natan, Hebrew University and MSRI.

Abstract: It is well known that when the Sun is at zenith precisely over Buenos Aires on odd numbered years (muslim calendar), the ray through the SW lower corner of the third tallest stone and the NE upper corner of the tallest stone in Stonehenge (Salisbury Plain, Wiltshire, S. England) points straight at Neptune's moon Naiad (discovered 1989, Voyager 2). This fact is so stunning it cannot be due to chance alone. It must be a sign from the Gods that they want us to study astrological lineups.

We therefore pick a knot, given as a specific embedding of S1 in R3, and count the number of "Stonehenge-inspired chopstick towers" that can be built upon it; namely, the number of delicate arrangements of chopsticks whose ends are lying on the knot or are supporting each other in trivalent corners joining three chopsticks each, so that each chopstick is pointing at a different pre chosen point in heaven that has a high mythical meaning.

Quite amazingly, when these stellar webs are counted correctly, the result is a knot invariant valued in some space of diagrams, deeply related to certain aspects of Lie theory and of the theory of Hopf algebras. We will touch on the former and dwelve into the latter, finding that if the Stonehengians had taken themselves seriously some 4,000 years ago, they would have been forced to discover quasi-Hopf algebras.

a Stonehenge-inspired chopstick tower.

This abstract is at http://www.math.toronto.edu/~drorbn/Talks/Riverside-000429/.

The handout for this lecture is at http://www.math.toronto.edu/~drorbn/Talks/UCB-000420/.