CS 85/185
Spring 2007

Introduction to
Computational
Topology


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Schedule

Date Day  #  Lecture Topics Links Handouts
05/29 T 17 Presentations.    
05/24 Θ 16 Presentations.    
05/22 T   No class. Work on projects!   Presentation papers:
Coordinate-free
Sensor networks
Splitting
Greedy generators
05/17 Θ 15 PL functions; Morse lemma; Euler characteristic Inside the Klein bottle  
05/15 T 14 Persistence algorithm; Morse functions Morse theory
Gert Vegter's Animations:
Bulged Sphere
Torus Levels
Attaching a saddle
Computing Persistent Homology
05/10 Θ 13 Filtrations; theory of persistent homology   Barcodes
05/08 T 12 Nerve Lemma; Complexes: Čech, Vietoris-Rips, α, witness Alpha Shapes Witness complex
6. Homology
05/03 Θ 11 Field coefficients; Duality; Data structures;   Quad-Edge (with Code)
Edge-Facet (from Ernst Mücke's thesis)
05/01 T 10 Hauptvermutung; Poincaré Conjecture; Computing Homology Poincaré Conjecture @ Clay Institute
Scientific Comic Books
5. Homotopy
Poincaré Conjecture
Topo the World
Homework Four
04/26 Θ 9 Homology – The Poincaré Conjecture Proved Hardcopy handouts:
– The Mathematics of Three-dimensional Manifolds
– The Shapes of Space
04/24 T 8 Homotopy; Markov's undecidability   4. Group Theory
Homework Three
Markov's Proof
04/19 Θ 7 Finitely generated groups; presentations; functors    
04/17 T 6 Groups; subgroups; factor groups   Homework Two
04/12 Θ 5 Triangulation; orientability; Euler characteristic   3. Simplicial Complexes
04/10 T 4 Simplicial complexes; subcomplexes   Homework One
04/05 Θ 3 Conway's ZIP; sphere eversions; k-simplex Smale's Paradox
The Optiverse
Outside In
Conway's ZIP
Max's Eversion
04/03 T 2 Manifolds; basic 2-manifolds   2. Surface Topology
03/29 Θ 1 Introduction; topological spaces   1. Point Set Topology
0. Introduction

 

Computer Science
Dartmouth College