MAT 530 Topology, Geometry I, Fall 2012.

  • Textbook :
    O.Ya.Viro, O.A.Ivanov, N.Yu.Netsvetaev, V.M.Kharlamov, Elementary Topology: Problem Textbook, AMS, 2008.
    The book is available in the campus bookstore (but can certainly be found for less money elsewhere). It is the required text. Parts of the homework will be assigned from it, and there will be required readings.
  • Homework: weekly assignments will be posted on Blackboard ( Homework will constitute a significant part of your course grade.

  • Syllabus:
    1. General topology
      • Topological structure in a set
      • Metric spaces
      • Subspaces of a topological space
      • Continuous maps
      • Homeomorphisms
      • Connectedness
      • Separation axioms
      • Countability axioms
      • Compactness
      • Sequential compactness
      • Product of topological spaces
      • Quotient topology
    2. Fundamental group and coverings
      • Homotopy
      • Fundamental group and high homotopy groups
      • Dependence of fundamental group on the base point
      • Simply-connectedness
      • Coverings
      • Calculations of fundamental group using universal coverings
      • Behavior of fundamental group under a continuous map
      • Classification of coverings
      • CW-complexes
      • Applications of fundamental group
    3. Manifolds
      • Topological manifolds
      • One-dimensional manifolds
      • Triangulated two-dimensional manifolds

    Students with Disabilities: If you have a physical, psychological, medical, or learning disability that may impact on your ability to carry out assigned course work, you are strongly urged to contact the staff in the Disabled Student Services (DSS) office: Room 133 in the Humanities Building; 632-6748v/TDD. The DSS office will review your concerns and determine, with you, what accommodations are necessary and appropriate. A written DSS recommendation should be brought to your lecturer who will make a decision on what special arrangements will be made. All information and documentation of disability is confidential. Arrangements should be made early in the semester so that your needs can be accommodated.