# Reading course Algebraic topology, fall 2013

The planning of the reading course is as follows. There will be 6 meetings (optional; all but one on Friday mornings), and 6 related homework sets. The meetings take place in Room Sn 402.

 Meeting: Reading: Homework deadline: 20 Sep, 11:15-13:00 Section 1 of syllabus 1 Oct 1 Oct, 15:45-17:30 (!) Section 2 of syllabus 18 Oct 18 Oct, 11:15-13:00 Section 3 of syllabus 1 Nov 1 Nov, 11:15-13:00 Sections 1.4, 2.1 and 2.2 of Szamuely's book 15 Nov 15 Nov, 11:15-13:00 Section 2.3 of Szamuely's book 6 Dec 6 Dec, 11:15-13:00 Section 2.4 of Szamuely's book 20 Dec

In this course we will treat 2 important methods/techniques in topology and geometry: (1) singular homology, (2) covering spaces. We shall try to emphasise both formal/abstract properties and concrete examples. Part (1) will end with a discussion of the famous Brouwer fixpoint theorem in arbitrary dimension, and the hairy ball theorem.

Part (1) will be based on some chapters of the lecture notes 'Algebraic topology' by Prof. E. Looijenga. Other very useful references are Chapter IV of G.E. Bredon, Topology and Geometry, Graduate Texts in Mathematics 139, and Chapter 2 of A. Hatcher, Algebraic Topology.

Part (2) will be based on Sections 1.4 and 2.1--2.4 of the book Galois groups and fundamental groups by Tamas Szamuely. A set of errata is available at the author's website.

Prerequisites: the local courses Algebra 1--2, Linear Algebra 1--2, Topology (or their equivalents).

The solutions to the homework exercises will be graded ++ (very good), + (good), +- (not so good) or - (poor). After the course is over there will be an oral exam discussing a random subset of the semester's homework exercises. The final grade (a half-integer between 1 and 10) is meant to reflect the student's performance on the semester's homework exercises, as well as her or his progression on these as measured during the oral exam. The exam takes place in office Sn240.

The course is worth 6 EC.

The teaching assistant of this course is Stefan van der Lugt. Solutions to the homework sets need to be given to him; mailbox in the common room, or by email: zstefanzvdlugtz at gmailz dot comz (remove the z's).

Here is an exercise sheet for Part (1).

 Homework deadline: Homework: 1 Oct Exercises 1--5 from sheet (1) 18 Oct Exercises 6, 8, 9, 10 and 11 from sheet (1) 1 Nov Exercises 12, 16, 17, 18, 19 from sheet (1). Replace 'In class we have seen' from Exercise 17 by 'In the syllabus it is proved' 15 Nov The exercises from this sheet. 6 Dec The exercises from this sheet. 20 Dec The exercises from this sheet.

### Schedule oral exams

 January 27 January 28 Other date?? 10:00-10:30 Barucchieri Joshi (20 feb) 10:30-11:00 Hommelberg Jespers Sloof (20 feb) 11:30-12:00 Koymans van Mulligen Zarabara 12:00-12:30 Noordman Pham (20 feb) 13:00-13:30 Pijpers Chicas Reyes Ruijter 13:30-14:00 Rodriguez (20 feb) 14:30-15:00 Tillij Schouten Hekking (20 feb) 15:00-15:30 Tonkelaar Wols 16:00-16:30 16:30-17:00 Schipper 17:00-17:30 van Munster