Huxley, Room 623
180 Queen's Gate
London SW7 2AZ
180 Queen's Gate
London SW7 2AZ
Steven Sivek
Imperial College Department of MathematicsS4D3: 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(S_{g}) (§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 H_{1}(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(S_{g}) (§6.1–6.3.2) | Andrea |
03.02 | Dehn-Nielsen-Baer theorem, metrics on π_{1}(S) (§8.1–8.2.3) | Steven |
10.02 | Proof of the Dehn-Nielsen-Baer theorem (§8.2.4–8.2.7) | Danica |