18.906, Fall, 2009


Lecture: MWF, 11:00, 2-131

Office hours: generally Wednesdays, 3:00 - 5:00, 2-237

This is a second course in Algebraic Topology. Roughly, I hope to cover the following topics.

  • Vector bundles and fiber bundles
  • Fibrations and homotopy groups
  • Spectral sequences
  • Hurewicz Theorem
  • Characteristic classes
  • Obstruction theory

    The prerequisite is exposure to the fundamental group, homology, cohomology, cup products.
    The grade will be based on several homework assignments and an oral exam.

    Some references:

    Milnor and Stasheff, Characteristic Classes
    Husemoller, Fibre Bundles
    Atiyah, K-theory
    Spanier, Algebraic Topology
    Whitehead, Homotopy Theory
    Bott and Tu, Differential Forms in Algebraic Topology

    Some notes:
    Notes on Universally closed maps.
    Notes on Cofibrations.
    A paper by Arne Strom about fibrations.
    Notes on the Serre spectral sequence.

    PS1, due Monday, February 23 in class.
    PS2, due Monday, March 16 in class.
    PS3, due Monday, April 13 in class.
    PS4, due Friday, May 8 in class.


    Oral Exam schedule

    Friday 15 May
    11:00 Cotton Seed

    Monday 18 May
    11:00 Gabriel Bujokas
    1:00 Tirasan Khandhawit
    2:00 Alex Pereira

    Tuesday 19 May
    2:00 Galina Dobrovolska
    3:00 Philip Tynan
    4:00 Charmaine Sia

    Wednesday 20 May
    11:00 George Tucker
    2:00 Rune Haugseng
    5:00 Thanasin Nampaisarn

    Haynes Miller