Algebraic Topology

Algebraic Topology


Algebraic Topology I (Autumn 2017)

This will be an introductory course in algebraic topology, intended for upper-level undergraduates and beginning graduate students.

Topics covered include:

  • the fundamental group,
  • singular homology,
  • cell complexes and cellular homology,
  • universal coefficients and the Eilenberg-Steenrod axioms. 

Along the way we will introduce the basics of homological algebra and category theory.

  • Lecture Notes for the course are here.
  • The Problem Sheets are here.
  • Here is a page intended for current students enrolled in the class. It contains the solutions to the Problem Sheets and other miscellaneous information. (You need a password to enter.)

Algebraic Topology II (Spring 2018)

This is a continuation course to Algebraic Topology I.

Topics covered include:

  • products in homology (the Eilenberg-Zilber Theorem and the Künneth Formula),
  • cohomology (the ring structure and Poincaré duality),
  • topics in homotopy theory (including the classical theorems of Serre, Hurewicz, Blakers-Massey and Whitehead.)

I will again produce full lecture notes.