Curvature and Computation
Group Theory
2014-12-08 v2 Geometric Topology
Abstract
When undergraduates ask me what geometric group theorists study, I describe a theorem due to Gromov which relates the groups with an intrinsic geometry like that of the hyperbolic plane to those in which certain computations can be efficiently carried out. In short, I describe the close but surprising connection between negative curvature and efficient computation. This theorem was one of the clearest early indications that applying a metric perspective to traditional group theory problems might lead to new and important insights.
Keywords
Cite
@article{arxiv.1411.7306,
title = {Curvature and Computation},
author = {Jon McCammond},
journal= {arXiv preprint arXiv:1411.7306},
year = {2014}
}
Comments
10 pages, expository article; version 2 clarifies some ambiguous language on computational complexity and corrects a passing musical reference from Stravinsky to Prokofiev