Week |
Date of Tuesday |
Tuesday |
Friday |
Lecture notes |
Comments |

3 |
Oct. 14 |
Outline of course. Classification of surfaces. |
Loops and arcs. Cutting, gluing. Reflections, twists,
half-twists. |
Tuesday
Friday |
How many Mobius bands can you embed in $\RR^3$? |

4 |
Oct. 21 |
$\Homeo(S)$, $\MCG(S)$, $\Simple(S)$. Sphere and disk. |
Annulus and pants. Geometric intersection number.
Bigon criterion. |
Tuesday
Friday |
Why is the $\alpha$-cover of S an annulus? |

5 |
Oct. 28 |
$\Simple(T)$, $\PML(S)$ and $\PML(T)$. |
$\Teich(T)$. The hyperelliptic element. |
Tuesday
Friday |
Friday lecture cut short due to technical
difficulties. |

6 |
Nov. 4 |
$\MCG(T)$. Alexander method. Braid relation. |
Elliptic, parabolic, hyperbolic. Examples. $\Teich(S)$.
Nielsen-Thurston classification. Braid relation. |
Tuesday
Friday |
The hyperelliptic generates the center of $\MCG(T)$. |

7 |
Nov. 11 |
Relations, hyperelliptic in MCG(S_2).
Statement of Dehn-Lickorish theorem.
Genus zero case. Surgery of arcs. |
Surgery of loops. Finish proof of theorem. |
Tuesday
Friday |
$2g + 1$ twists suffice. |

8 |
Nov. 18 |
$\Curves(S)$. Pants decompositions. Filling. Distance. |
Statement of Ivanov's theorem. Special cases. Hyperelliptics.
Farey graph, $\Farey$. |
Tuesday
Friday |
Harmonic vs hyperbolic Farey graph. |

9 |
Nov. 25 |
$\Aut(\Farey)$. Link of a simplex. Crawling. Duality.
Action of twists on $\Farey$. |
Large and small links. Arc complex. Pentagon lemma. |
Tuesday
Friday |
Combinatorial data determines topological. |

10 |
Dec. 2 |
Ivanov in genus zero. |
Pentagon in $S_{1,2}$. Second pentagon lemma. |
Tuesday
Friday |
What does $C(S_{0,5})$ look like? |

11 |
Dec. 9 |
Finished second pentagon. Combinatorial duals. Bracelets.
Bicolored Farey graph. |
Finish Ivanov's theorem. A hint of Masur-Minsky I.
$\delta$-hyperbolicity. Systoles. |
Tuesday
Friday |
How many different colored pentagons are there? |