INTRODUCTORY TOPOLOGY I.

office: 713 Van Vleck
e-mail: maxim@math.wisc.edu
office hours: Mo, 1-5 PM, or by appointment.

CLASS SCHEDULE: MWF 12:05 -12:55, Room VAN VLECK B211.

CLASS HOMEPAGE: http://www.math.wisc.edu/~maxim/MATH751.html

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

READING SOURCES:

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

GRADE: Midterm: 40%, Final Exam: 60%.

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

• HW 1: Fundamental group.
  
• HW 2: Van Kampen's theorem.
  
• HW 3: Classification of surfaces.
  
• HW 4: Covering spaces.
  
• Midterm Exam: version 1, version 2.
  
• HW 5: Singular homology.
  
• HW 6: Degrees.
  
• HW 7: CW complexes, Cellular homology.
  
• HW 8: Homology with coefficients. Euler characteristic. Lefschetz fixed-point theorem.
  
• Final Exam