Resources

References for Mathematical Terms & Concepts

• MathWorld
• PlanetMath
• Wikipedia

Course Notes

• 6. Homology
• 5. Homotopy
• 4. Group Theory
• 3. Simplicial Complexes
• 2. Surface Topology
• 1. Point Set Topology
• 0. Introduction

Homeworks

• Homework Four
• Homework Three
• Homework Two
• Homework One

Supplementary Handouts

• Coordinate-free coverage in sensor networks with controlled boundaries via homology – Vin de Silva and Robert Ghrist
• Homological Sensor Networks – Vin de Silva and Robert Ghrist
• Splitting (complicated) surfaces is hard – Erin Chambers, Éric Colin de Verdière, Jeff Erickson, Francis Lazarus, and Kim Whittlesey
• Greedy optimal homotopy and homology generators – Jeff Erickson and Kim Whittlesey
• Computing Persistent Homology – Afra Zomorodian and Gunnar Carlsson
• Barcodes – Robert Ghrist
• Witness complex – Vin de Silva and Gunnar Carlsson
• Quad-Edge (with Code) – Dani Lischinski
• Edge-Facet – from Ernst Mücke's thesis
• Poincaré Conjecture – John Milnor
• Topo the World – Jean-Pierre Petit and John Murphy
• The Poincaré Conjecture Proved. Science Magazine, April 26, 2007.
• Collins, G. P. The Shapes of Space. Scientific American, 291(1), 2004. (Hardcopy)
• Thurston, W. P. and Weeks, J. R. The Mathematics of Three-dimensional Manifolds. Scientific American, 251(1) (1984). (Hardcopy)
• Markov's Proof – A. A. Markov
• Max's Eversion – Nelson Max and William H. Clifford, Jr.
• Conway's ZIP – George Francis and Jeff Weeks

Software

• CHomP
• PLEX
• RoffView