Introduction to Topology

Martin Lotz – The University of Warwick

General Information

Lecture Monday 11-12 MS.01
Tuesday 12-13 H0.51
Wednesday 9-10 MS.01
Support class (Bigazzi / Te Winkel) Monday 15-16 LIB2(L)
Support class (Bigazzi / Te Winkel) Tuesday 13-14 B2.04/5

 

Content

This module covers topological spaces and their properties, homotopy, the fundamental group, Galois correspondence, universal covers, free products, and CV complexes.

The course will follow largely the first chapter of

An electronic version of the book is freely available on the author’s web page, and a printed version should be available in the library or the campus bookshop.

Intended Learning Outcomes

Upon completion of this course, you will know how to distinguish spaces by means of topological invariants. You will be able to construct spaces by gluing and to prove that in certain cases the result is homeomorphic to a standard space. In addition, you will be able to construct examples of spaces with given properties (e.g., compact but not connected or connected but not path connected).

Lecture Notes

Brief lecture notes will be published regularly, usually in the days after each lecture. They will be available on the dedicated Lectures page.

Exercises

Weekly problem sheets can be found on the Exercises page. Assessed work will be 15% of your mark. Of this, 2% (at most) may be earned every week (starting the second week) by turning in one of the three indicated exercises. These will be marked by a TA with a score of 0, 1, or 2. Please let me know if any of the problems are unclear or have typos.

Homework solutions must be placed in the dropoff box (near the front office), by 14:00 on Thursdays. No late work will be accepted. Please write your name, the date, and the module code (MA3F1) at the top of the page. If you collaborate with other students, please include their names.

Solutions typeset using LaTeX are preferred. Each problem should require at most one side of one page. If you find you need more space then write out a complete solution and then rewrite with conciseness in mind.

Exams

Unless stated otherwise, all the covered material will be relevant for the exam. Information on exams and a link to previous exams is contained in the Exams page.

Additional literature

The following references are not needed for the course, but can provide additional information and perspective for those interested.

  1. M.A.Armstrong. Basic Topology. Springer
  2. Glen E. Bredon. Topology and Geometry. Springer.
  3. E. Spanier. Algebraic Topology. Springer.