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Knots play a central role in the modern study of the topology of three-dimensional manifolds. In this graduate topics class, we'll see how knots can be used to construct and understand three-manifolds, and we'll also study the rich algebraic theory of knot invariants, including recent developments that have shaped the field in the past decade.
The course should be accessible to anyone with a basic background in algebraic topology (along the lines of Math 611). I'm hoping that it will be interesting and useful to anyone of an algebraic or topological bent.
Topics I plan to cover include:
I will begin the class loosely following the book Knots, Links, Braids, and 3-Manifolds by Prasolov and Sossinsky, but will frequently diverge from it. I'll provide additional sources for further reading, as appropriate.
Course syllabus containing all of the above information and more.