S4D3: Graduate seminar on advanced geometry

• Wintersemester 2016/17, Fr 12-14 in 1.007
• Office hours: by appointment, 1.029

This is a seminar on mapping class groups of surfaces. These are the groups of isotopy classes of homeomorphisms of a surface; they are ubiquitous in low-dimensional topology, and they are interesting as algebraic objects of study in and of themselves. We will follow part 1 of the following book:

• Benson Farb and Dan Margalit, A primer on mapping class groups (ULB)

It is available as a free eBook via the ULB link if you are connected to the University of Bonn network.

Lecture schedule:

21.10	Surfaces, simple closed curves, change of coordinates principle (§1)	Steven
28.10	Mapping class groups, simple examples (§2.1–2.2)	Zhicheng
04.11	Dehn twists, intersection numbers (§3.1–3.2)	Paul
11.11	The Alexander method, the center of Mod(Sg) (§2.3, 3.3–3.4)	Gabriele
18.11	Relations between Dehn twists, capping and cutting (§3.5–3.6.3)	Danica
25.11	Outline of Dehn-Lickorish theorem, the curve complex (§4–4.1)	Andrea
02.12	The Birman exact sequence (§4.2)	Zhicheng
09.12	Finite generation (§4.3–4.4)	Steven
16.12	The lantern relation and H1(Mod(S)); Wajnryb's presentation (§5.1–5.2.1)	Paul
13.01	Finite presentability (§5.3)	Gabriele
20.01	The symplectic representation of Mod(Sg) (§6.1–6.3.2)	Andrea
03.02	Dehn-Nielsen-Baer theorem, metrics on π1(S) (§8.1–8.2.3)	Steven
10.02	Proof of the Dehn-Nielsen-Baer theorem (§8.2.4–8.2.7)	Danica