INTRODUCTORY TOPOLOGY I.

office: 713 Van Vleck
e-mail: laurentiu.maxim@gmail.com
office hours: Tue 11-12, 4-5

CLASS SCHEDULE: TuTh 2:30PM -3:45PM, Room VAN VLECK B211.

CLASS HOMEPAGE: http://www.math.wisc.edu/~maxim/751f14.html

DESCRIPTION: Fundamental group; Classification of compact surfaces; Covering spaces; Homology; CW complexes.

READING SOURCES:

• Allen Hatcher: Algebraic Topology, available here.
• William Massey: A Basic Course in Algebraic Topology
• James Munkres: Topology, 2nd ed.

GRADE:

Homework and class participation: 25%, Midterm: 25%, Final Exam: 50%.
As part of class participation, each student is expected to type up a week worth of lecture notes.
The midterm exam will take place on October 21, during the usual lecture time.

HOMEWORK: it will be assigned regularly and will be the main source of problems appearing in the exams.

• HW 1: Basic homotopy theory. Fundamental group. (due September 25)
  
• HW 2: Fundamental group. Van Kampen's theorem. (due October 7)
  
• HW 3: Classification of surfaces. (due October 16)
  
• HW 4: Covering spaces. (due November 4)
  
• HW 5: Introduction to homology. (due November 13)
  
• HW 6: Homology computations. (due November 25)
  
• HW 7: Degrees. CW complexes. Cellular homology. (due December 4)
  
• HW 8: Homology with coefficients. Euler characteristic. Lefschetz fixed-point theorem. (due December 11)
  
• Final Exam (takehome exam, due December 18)