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18.917

Topics in Algebraic Topology

3-0-9 units · Graduate

Content varies from year to year. Introduces new and significant developments in algebraic topology with the focus on homotopy theory and related areas.

Fall 2007 · Topics in Algebraic Topology: The Sullivan Conjecture

The goal of this course is to describe some of the tools which enter into the proof of Sullivan's conjecture.

Readings

  • Schwartz, Lionel. Unstable Modules over the Steenrod Algebra and Sullivan’s Fixed Point Set Conjecture . Chicago, IL: University of Chicago Press, 1994. ISBN: 9780226742021.
    Listed reading
  • LEC #: 2-5 · READINGS: May, J. P. “A General Algebraic Approach to Steenrod Operations.” Lect Notes Math 168 (1970): 153-231.
    Reading assignment
  • LEC #: 6-7 · READINGS: Schwartz, sections 1.6 and 1.7.
    Reading assignment
  • LEC #: 7-10 · READINGS: Kuhn, N. J. “Generic Representation Theory of the Finite General Linear Groups and the Steenrod Algebra: I.” Amer J Math 116 (1994): 327-360.
    Reading assignment
  • LEC #: 12 · READINGS: Serre, J.-P. “Cohomologie modulo 2 des complexes d’Eilenberg-MacLane.” Commentarii Mathematici Helvetici 27 (1953): 198-231.
    Reading assignment
  • LEC #: 13 · READINGS: Milnor, John. “The Steenrod Algebra and its Dual.” Annals of Mathematics 67 (1958): 150-171.
    Reading assignment
  • LEC #: 14 · READINGS: Schwartz, section 1.7.
    Reading assignment
  • LEC #: 15 · READINGS: Schwartz, section 1.8.
    Reading assignment
  • LEC #: 16-20 · READINGS: Schwartz, chapters 2 and 3.
    Reading assignment
  • LEC #: 25 · READINGS: Dror-Farjoun, E., and J. Smith. “A Geometric Interpretation of Lannes’ Functor T.” Israel J Math 66 (1989).
    Reading assignment
  • LEC #: 27 · READINGS: Mandell, M. “E-infinity Algebras and p -adic Homotopy Theory.” Topology 40 (2001): 43-94.
    Reading assignment
  • LEC #: 31-32 · READINGS: Geometric Topology: Localization, Periodicity and Galois Symmetry: The 1970 MIT Notes of Dennis Sullivan ( PDF - 1.3 MB ) ↗
    Reading assignment
  • LEC #: 33 · READINGS: Miller, H. R. “The Sullivan Conjecture on Maps from Classifying Spaces.” Ann of Math 120 (1984): 39-87.
    Reading assignment
  • LEC #: 34 · READINGS: Dwyer, W. G., H. R. Miller, and C. W. Wilkerson. “The Homotopic Uniqueness of BS 3, in ‘Algebraic Topology, Barcelona 1986.’” Lecture Notes in Math 1298 (Springer, Berlin, 1987): 90-105.
    Reading assignment
  • LEC #: 35-37 · READINGS: Schwartz, chapters 5 and 6.
    Reading assignment

Prerequisites & course information

Prereq: 18.906 Acad Year 2027-2028: G (Spring) Acad Year 2028-2029: Not offered 3-0-9 units Can be repeated for credit.

Sources