Topology Seminar for 2/20/2003

Adam Sikora
Institute for Advanced Study

Analogies between number theory and 3-dimensional topology

Abstract

We will describe some surprising similarities between 3-dimensional topology and number theory observed by B. Mazur, and others. These similarities can be summarized by saying that knots are like prime numbers and 3-manifolds like number fields. We prove results both in topology and in number theory which further extend these analogies.