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:
– Coordinatefree
– 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, VietorisRips, α, witness

– Alpha Shapes

– Witness complex
– 6. Homology

05/03 
Θ 
11 
Field coefficients; Duality; Data structures;


– QuadEdge (with Code)
– EdgeFacet (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 Threedimensional 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; ksimplex 
– Smale's
Paradox
– The Optiverse
– Outside In

– Conway's ZIP
– Max's Eversion

04/03 
T 
2 
Manifolds; basic 2manifolds 

– 2. Surface Topology

03/29 
Θ 
1 
Introduction; topological spaces 

– 1. Point Set Topology
– 0. Introduction
