The Computational Complexity of Geometric Topology Problems

The Computational Complexity of Geometric Topology Problems - Greg Kuperberg

Greg Kuperberg
University of California, Davis
September 24, 2012

This talk will be a partial survey of the first questions in the complexity theory of geometric topology problems. What is the complexity, or what are known complexity bounds, for distinguishing n-manifolds for various n? For distinguishing knots? For recognizing a sphere, or the unknot? The survey will be a warmup to my own contribution, which is the fact that knottedness is in NP, assuming the generalized Riemann hypothesis.