Triangulations In Dimension Three: Algorithms And Geometric Structures

Grant number: DP1095760 | Funding period: 2010 - 2013

Completed

Abstract

Perelman recently won a Fields medal for the solution of the geometrisation and Poincare conjectures on three-dimensional spaces, using a very deep heat flow method to find optimal geometries on these spaces. The project will develop a new constructive approach to building these optimal geometric structures. This will lead to effective algorithmic methods to distinguish three-dimensional spaces, with applications to the study of knots and links (for example, knotted DNA molecules) and to mathematical physics. The project will also provide new techniques to study important problems in the classification of three-dimensional spaces, such as the virtual Haken conjecture.