The Generalized Knot Complement Problem by Prof. David Futer, Temple University

The Generalized Knot Complement Problem by Prof. David Futer, Temple University, Friday March 8, 1:00 – 1:50pm, North Science Building 015, Wachenheim, Mathematics Seminar, Class of 1960 Scholar

Abstract: In 1908, Tietze posed the provocative question of whether a mathematical knot — a knotted rope, with its ends spliced together — is completely determined by the topological shape of the empty space that surrounds the knot. After being open for 80 years, this question was solved in 1988, and we know the answer is: Yes.

Since that time, mathematicians have been stumped by the question of whether the same property holds for knots in general 3—dimensional spaces. Given a 3—dimensional manifold M, is a knot in M entirely determined by the space that surrounds it in M? I will discuss some recent work on this question using hyperbolic (negatively curved) geometry. This is joint work with Jessica Purcell and Saul Schleimer.

This talk is for colloquium credit.