Math 8306 - Algebraic Topology - Fall 2010

Instructor: Anar Akhmedov

Lectures: MWF 10.10 - 11.00am in Vincent Hall 206.

E-mail: akhmedov@math.umn.edu

Office Hours: Friday 11.05am - 12.00pm and 1.00 - 2.00pm. If you have questions, I encourage you to come to my office hours. This would be the best time to talk to me and address questions you have about the course material, homework assignments, grading, exams, etc. My office is in room 355 of the Vincent Hall.

Prerequisites: Math 8301 or instructor's consent.

Textbook: Algebraic Topology, by Allen Hatcher. The textbook is available at the University bookstore, and also on reserve in the Mathematics Library. Our textbook is also available free online, at http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Other Recommended Textbooks
Title Author(s), Publ. info Location
Topology and Geometry G. Bredon On reserve in math library
Topology from a differential point of view J. Milnor On reserve in math library
Differential forms in Algebraic Topology R. Bott and L. P. Tu On reserve in math library
Algebraic Topology W. Fulton On reserve in math library
Algebraic Topology E. Spanier On reserve in math library

Course Outline: This is a first course in algebraic topology. The fall semester we plan to cover Chapters 0 - 3 of the textbook. The main topics are: homotopy, fundamental group, covering spaces, homology, and cohomology.

Web page: http://www.math.umn.edu/~akhmedov/M8306.html.

Grading: The course grade will be based on seven homework assignments and a comprehensive take-home final, with the following weights:

  • 70% Homework
  • 30% Take Home Final

    Exams: There will be a comprehensive take-home final examination which will worth 30 points (30% of the final course grade). TAKE HOME FINAL
    DUE: by noon Monday, December 20

    Homework: There will be 7 homeworks in this course, each worth 10 points. Homework will be a fundamental part of this course, and will be worth 70 points (70% of the course grade). NO LATE HOMEWORK WILL BE ACCEPTED. The first homework assignment will be due on September 20. Please staple your homework before handing it in. If you have questions about the homework, it is best to ask during my office hours.

    Assignment Problems from the Text
    Homework 1
    due Sept 20
    Chapter 0
    Problems 10, 14, 16, 18, 20, 24.
    Homework 2
    due Oct 4
    Chapter 1
    Section 1.1: Problems 3, 10, 12, 15, 17, 18
    Homework 3
    due Oct 20
    Chapter 1
    Section 1.2: Problems 2, 3, 4, 6, 9, 14, 16
    Section 1.3: Problems 2, 3, 4, 9, 14, 20, 23
    Homework 4
    due Nov 8
    Chapter 2
    Section 2.1: Problems 4, 7, 8, 9, 11, 12, 13, 14.
    Homework 5
    due Nov 24
    Chapter 2
    Section 2.1: 17, 20, 22, 29.
    Section 2.2: Problems 2, 4, 10.
    Homework 6
    due Dec 8
    Chapter 2
    Section 2.2: Problems 11, 14, 15, 19, 21, 22, 23, 24, 36.
    Homework 7
    due Dec 15
    Chapters 2 and 3
    Section 2.2 Problem 38, 39
    Section 3.1: Problems 1, 3, 6a.