Proseminar: Topology & Groups

The proseminar meets Fridays, 15-16:30, in 67-442. It consists of lectures given by the participants.

We will follow Marc Lackenby's notes Topology & Groups.

Credit can be given towards honours course work. The final grade is a function of lectures given and class participation. Each lecture should stay well within the time limit of 90 minutes, and allow time for questions and discussion. Each lecture will be assessed in equal parts for clarity, demonstrated understanding of the material, and contents chosen from the notes. The lectures are not expected to cover the entire contents of the notes, but to highlight and explain the main points of each section. The participants are expected to read ahead before each lecture, and to work through the parts of the notes that were not covered in lectures.

An excellent collection of exercises can be found on Marc's web-site. They form an optional component of this proseminar and are highly recommended. The exercise sheets are linked here: 1, 2, 3, 4, 5, 6, 7.


Friday, 4 March
Stephan Tillmann: I.2 + II.1 (Simplicial Complexes, Homotopy)
Friday, 11 March
Sam Mellick: II.2 (The Simplicial Approximation Theorem)
Friday, 18 March
Matt Spong: III.1 (The definition of the fundamental group)
Friday, 25 March
Mitchell Watt: III.2-4 (More on fundamental groups)
Friday, 1 April
April Fool's Day Public Holiday
Friday, 8 April
Tom Chappell: IV.1-4 (Free groups)
Friday, 15 April
Mitchell Watt: V.1-3 (Group presentations)
Tuesday, 19 April
Amir Moghaddam: V.4 (The Seifert-van Kampen Theorem) (12:00-13:30 in Steele 3-323)
Friday, 22 April
Good Friday
Friday, 29 April
Mid-semester break
Friday, 6 May
Mitchell Watt: I.3 + V.5 (Cell complexes, Topological Applications)
Friday, 13 May
Tom Chappell: VI.1 (Definition and basic properties of covering spaces)
Friday, 20 May
Matt Spong: VI.2-3 (The inverse image of the basepoint; Uniqueness of covering spaces)
Friday, 27 May
Sam Mellick: VI.4 (Construction of covering spaces)
18 April 2011