## The computational complexity of geometric topology problems

**Greg Kuperberg**

**Monday, September 23, 2013**

4:00pm 5130 Upson Hall

__Abstract:__

### I will survey some of the results and questions about the complexity
of geometric topology problems, specifically in the sense of complexity
classes. What is the complexity of distinguishing n-manifolds for various
n? Of distinguishing knots? Of recognizing a sphere, or the unknot? Last but not least I will discuss some of my own contributions: Unknot
and 3-sphere recognition are in coNP assuming the RIemann hypothesis;
approximating the Jones polynomial is #P-hard; and complexity results for
certain higher-dimensional problems.

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