THE KONTSEVICH INTEGRAL AND COVERING SPACES

A new field was created in 1984 when, famously, Vaughan Jones discovered a new polynomial invariant of knots. In the years that immediately followed there appeared a confusing proliferation of similar constructions. The Yang-Baxter equation proved to be the essential tool that led to the systematization of these ideas within the algebraic theory of quantum groups. In this talk I want to give a taste of what has happened in the field in the twenty years since these first developments by describing a key recent result: the rationality of the Kontsevich integral.

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