This is the project page for the Australian Research Council funded Discovery Project

Triangulations in dimension three:
algorithms and geometric structures

ARC Discovery Grant DP1095760
2010-2012

personnel

Chief Investigators:
Craig Hodgson (Melbourne)
Hyam Rubinstein (Melbourne)
Stephan Tillmann (Queensland 2010-2011; Sydney 2012)
Research Fellow:
Henry Segerman

summary

The aim is to constructively build the optimal geometric shapes for three-dimensional spaces and study their properties by new practical algorithms. It is known, by remarkable work of Perelman, that all three-dimensional spaces can be decomposed into pieces admitting uniform geometric structures. However a constructive way of finding these structures is not known. We will attack this problem by finding suitable ways of splitting each space into tetrahedra which carry the geometry. This will enable us to construct and implement new practical algorithms to recognise different three-dimensional spaces and to identify important surfaces in them, as needed in knot theory.

publications

preprints

work in progress

code contributions

conferences

2010
Algorithms, Algebra and Analysis in Four Dimensions, Brisbane, Australia (20-21 July)
2011
Geometry & Topology Down Under, Melbourne, Australia (11-22 July)

visitors

2010
Joel Hass (UC Davis) Melbourne: 20.1.-30.6.
Abigail Thompson (UC Davis) Melbourne: 20.1. - 30.6.
2011
Peter Scott (Michigan) Melbourne: 9.2.-16.3.
Hidetoshi Masai (Tokyo Institute of Technology) Melbourne: 9.7.-5.10.
Ian Agol (UC Berkeley) Queensland: 24.7.-27.7.
Joseph Maher (CUNY Staten Island) Queensland: 27.7.-8.8.
Bus Jaco (Oklahoma State) Queensland: 8.8.-16.8.
2012
Joseph Maher (CUNY Staten Island) Sydney: June/July

students

related links

related news


http://www.maths.usyd.edu.au/u/tillmann/DP1095760/
18 February 2012