18.917: Topics Algebraic Topology

Monday, Wednesday, Friday, 11:00, 2-147

This course will focus on the Adams spectral sequence and some classic applications in stable homotopy theory. These may include
  • the invariants of Hopf and Kervaire
  • the conjectures of Mahowald and Segal
  • the K-theoretic telescope conjecture

    Prerequisite: something like 18.906.

    Office hours: After class as announced. (Bring lunch!)

    If you're enrolled in the course, please fill out the Online subject evaluation for this course.

    Notes on triangulated categories.
    Notes on the cobar construction.
    Notes on the Kervaire invariant and the Hopf invariant on a Moore space.
    Notes on the Kervaire invariant and manifolds with corners.
    Fragment of a book: formal groups, the dual Steenrod algebra, cobordism comodules.

    Some resources

  • S. P. Novikov's "The methods of algebraic topology from the viewpoint of cobordism theory," pdf.
  • Harvey Margolis's "Spectra and the Steenrod Algebra," djvu.
  • Doug Ravenel's "Complex cobordism and stable homotopy groups of spheres," website.
  • Course notes from an old 18.917 on the vector field problem and associated homotopy theory, Part I and Part II.
  • Christian Nassau's charts.
  • Husemoller, Moore, and Stasheff, on Cotor, pdf
  • Miller and Wilkerson on vanishing lines, pdf.
  • Miller, "A localization theorem in homological algebra" pdf.
  • Miller, Comparing Adams spectral sequences, pdf.
  • Miller, Ravenel, and Wilson, "Periodic phenomena in the Adams-Novikov spectral sequence," pdf.
  • Course notes from an old 18.917 on complex oriented cohomology theories, pdf.
  • Miller, "Finite localizations," pdf.

    Haynes Miller
    2-237, 3-7569