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.

    The last part of the course is covered in the following text

    Topological manifolds (updated on 12/11), which is organized as a continuation of the main textbook.
  • Midterm exam will be on October 16 (Tuesday), in class. It will cover general topology up to product of topological spaces inclusively. Among the problems there will be theorems with proofs from the following list. No books or notes are allowed on exams.
  • Homework: weekly assignments will be posted on Blackboard (https://blackboard.stonybrook.edu/). Homework will constitute a significant part of your course grade.

    Homework 1 is due on 9/10 (postponed from 9/6).

    Homework 2 due on 9/13.

    Homework 3 due on 9/20. By Tuesday 9/18 revisit all the definitions in sections 2, 3, 4, 5, 6, 10 and 11. Be prepared for reproducing any of the definitions in writing.

    Homework 4 due on 9/26.

    Homework 5 due on 10/4.

    Homework 6 due on 10/11. By Tuesday 10/9 revisit all the definitions in sections 12 - 18. Be prepared for reproducing any of the definitions in writing.

    By Tuesday 10/30 revisit all the definitions and formulations of theorems in sections 21, 22 and 30.

    Homework 7 due on 11/1.

    On Tuesday 11/13 after the lecture one can make up the midterm exam.

    Homework 8 due on 11/15.

  • Final Exam will be on Monday, December 17, 11:15AM-1:45PM in room 183 of Earth and Space Sciences Building. Here is a very detailed program for the exam.
  • 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.