Algebraic Knot Theory - A Call for Action

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Contents

Abstract

We knot theorists have lots of algebraically-defined knot invariants, but they tell us just little about knots. In this manifesto we suggest a reason for the failure and the means to rectify it.

Algebraic Knot Invariants: What They Do and What They Don't

Definability and Knotted Trivalent Graphs

What We Seek - An "Algebraic Knot Theory"

The Kontsevich Integral of Knotted Trivalent Graphs

The Challenges