Math 281b: Introduction to algebraic and differential topology

Stanford University, ``Winter'' 2001


  • (1/22) Class is cancelled on Friday 1/26. We will have a makeup lecture at the end of the quarter if we haven't finished the syllabus.
  • (1/9) If you don't make it to the first day of class, please be sure to fill out this survey.
  • (1/5) Room change: this course will meet in room 380-380F.


    Michael Hutchings
    Tentative office hours: Mon, Wed, 1:00 - 2:30, Room 383M.


    Homework assignments will be posted here every couple of weeks. Doing exercises is essential for learning the material.

    HW#1, due 2/2. pdf ps

    Course goals

    We will continue the development of algebraic topology from 281a, with a heavy emphasis on the topology of manifolds. Most of the spaces that topologists study are manifolds, or at least are constructed out of manifolds in some way. We will see that special properties hold for the algebraic topology of manifolds, such as Poincare duality. Also some of the abstract notions of algebraic topology have a simple geometric interpretation in the special case of manifolds; for example, the cup product just corresponds to intersection of submanifolds. I will primarily, except for illuminating digressions as time permits, try to stick to basic ideas that I consider to be most essential as a foundation for further study and research in topology.

    Although this course is a continuation of 281a, we will begin with a brief review of homology and cohomology, and we will review other concepts as necessary as we go along.


    The list of topics here, and especially the schedule, are somewhat tentative. I will pass out a survey on the first day of the class to get an idea of everyone's background and goals, after which I may make some adjustments to the syllabus.


    The basic reference for this course is Bredon's Topology and Geometry. We will not follow this book too closely in the lectures; we will take a slightly more geometric point of view, and some of the later material is not covered there.

    Some additional references

    (just in case you aren't already familiar with them)
    Up to Stanford Graduate Mathematics.
    updated: 1/21/01