General Topology and Knot Theory, Math 5801 (class numbers 34617 and 34618),
Spring Semester 2020

Instructor: Sergei Chmutov

Classes: Monday, Wednesday, Friday 12:40--1:35 pm. at Journalism Bldg 274.

Carmen: https://carmen.osu.edu

TEXTBOOKS:
Main Textbook:

  • C.Kosniowski. A First Course in Algebraic Topology.
     Cambridge University Press. 1980, ISBN-13: 978-0521298643. ISBN-10: 0521298644.

    Additional books:

  • M.A. Armstrong. Basic Topology. Springer. 1997, ISBN-13: 978-0387908397, ISBN-10: 0387908390.
  • J. Munkres. Topology. Pearson, 2nd Edition. 2000, ISBN-13: 978-0131816299.   
  • C. Adams, R. Franzosa. Introduction to Topology: Pure and Applied. Pearson. 2007, ISBN-13: 978-0131848696.                           
  • C.Adams. The knot book. AMS. 1994, ISBN-13: 978-0821836781, ISBN-10: 0821836781.

    Grading: There will be weekly homework assignments (25%) and three midterms (25% each).
    GRADING SCALE:
    A A- B+ B B- C+ C C- D+ D
    90 87 83 80 77 73 70 67 63 60

    TOPICS:
    1. General (poit-set) topology.
          Topological spaces, Continuous functions, Induced and Quotient topology,
          Product spaces, Compact spaces, Hausdorff spaces, Connected spaces,
          Manifolds and surfaces, Classification of surfaces.
    2. Algebraic topology.
          Homotopy, Fundamental group, Seifert-Van Kampen theorem.
    3. Knot theory.
          Fundamental group of knot complement, Wirtinger presentation,
          Seifert surface, Alexander polynomial.

    Handouts:
    1. Quotient topology. 2. Surfaces and chord diagram. 3. Classification.