Differential Topology II, Math 7852 (class number 35523),
Spring Semester 2026

Instructor: Sergei Chmutov

Carmen: https://carmen.osu.edu

TEXTBOOKS:

  • J.W.Milnor and J.D.Stasheff Characteristic Classes.
    Princeton University Press 1974, ISBN: 0-691-08122-0.

    Additional books which may be used:

  • Michael Spivak: A Comprehensive Introduction to Differential Geometry, Vol.1--5.
    Publish or perish, 1999.
  • A.Hatcher Algebraic Topology. Cambridge University Press, 2002. ISBN:0521795400.
  • A.Hatcher Vector Bundles and K-Theory. 2003.
  • V.Guillemin and A.Pollack Differential topology. Prentice-Hall Inc., 1974.
  • M.W.Hirsch Differential topology. Springer-Verlag, 1976.

    Catalog Description: DeRahm and Cech cohomology; deRahm Theorem; Grassmannians; Stiefel-Whitney, Euler, Chern, and Pontryagin classes; Gysin sequence, Thom isomorphism; characteristic numbers, multiplicative sequences, Hirzebruch signature theorem; Chern-Weil Theory.

    Classes: Monday, Wednesday, Friday 12:40--1:35 pm. The classes will be in-person in Caldwell Lab 109.
    There will be no homework assignments and no exams in this course. The course will mostly consists of the student presentations. The topics for possible presentations will be announced in Carmen. They will follow roughly to the Milnor-Stasheff book with possible use of other sources. The grades will be based on the presentations and activity in the class discussion.



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