MT 808: Geometry/Topology I (Algebraic Topology)
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
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
Grade: Your final grade will be calculated according to HW
(50%) and Final (50%).