MT 808: Geometry/Topology I (Algebraic Topology)

Fall 2017

Time/Location: MWF 2-2:50, Maloney 560

Instructor: John Baldwin
Office: Maloney 545
Office Hours: TBA

Course Description: This course is a graduate-level introduction to algebraic topology. The overarching theme of the subject is to use algebra to study topology. More precisely, one assigns algebraic objects (numbers, groups, rings, etc.) to topological spaces such that topologically equivalent (i.e. homeomorphic) spaces are assigned isomorphic objects. Given such an assignment, one may then distinguish two topological spaces by showing that their corresponding algebraic invariants are not isomorphic. As we'll see, this turns out to be an extremely powerful idea for studying spaces and their properties. The topics we'll cover will include homotopy, fundamental group, covering spaces, homology, cohomology, and Poincare duality.

Prerequisites: Prerequisites are undergraduate algebra and point-set topology at the level of Munkres' Topology.

Textbook: The primary reference for this course will be Hatcher's Algebraic Topology. You should read the preface and Chapter 0 on your own, in the first week of the course. We'll cover most of the material in Chapters 0-3.

Assignments: There will be regular homework assignments (posted below) and a final exam. The homeworks will be collected and graded. Either use LaTeX or make sure that your writing is very neat and legible.

Grade: Your final grade will be calculated according to HW (50%) and Final (50%).