Math 490 Section TS3/TS4 (Topology of Surfaces) Fall 2007

The subject of this topics course is geometric/combinatorial topology. As such it complements the two other advanced undergraduate courses in topology and geometry (Math 423: Differential Geometry of Curves and Surfaces, and Math 432: Set Theory and Topology). The highlight of the course and our principal aim is the classification theorem for compact connected surfaces, which we will prove by an explicit combinatorial argument. Along the way we will encounter applications of ideas and techniques from geometric topology in a variety of other contexts: differential equations and vector fields, algebra, knot theory, graph theory and map colorings, to name a few.

Contents

• Instructor information
• Course information
• Homework, projects and exams information
• Grading Policy

Lecture Log and homework assignments

• Instructor: Prof. Jeremy Tyson
• Office Location: 330 Illini Hall
• Office Phone: 244-4132
• Email: tyson@math.uiuc.edu
• Office Hours: Wed 2:00-3:00, Thu 10:00-11:00

• Lecture Times: MonWedFri 9:00-9:50
• Lecture Location: 343 Altgeld Hall
• Course web site: http://www.math.uiuc.edu/~tyson/490f07.html.

• Textbook: Topology of Surfaces by L. C. Kinsey (Springer, 1993)
• Other recommended texts (on reserve at the Math Library):
  • A Combinatorial Introduction to Topology by M. Henle (Freeman and Co., 1979; reprinted by Dover, 1994)
  • A First Course in Geometric Topology and Differential Geometry by E. D. Bloch (Birkhauser, 1997)
  • The Knot Book by C. Adams (Freeman and Co., 1994)
  • Knots and Surfaces by D. W. Farmer and T. B. Stanford (AMS, 1996)
  • Intuitive Topology by V. V. Prasolov (American Mathematical Society, 1995)
  • Topology by J. R. Munkres (Prentice-Hall, 1975)

• Homework and projects: There will be regular homework assignments (approximately three per month). In addition, there will be one long-term project. Topics for the projects can come from a list which I will draw up; you are welcome to design your own project as well although it must receive my OK first.

  You are encouraged to work on the homework in groups, although each student should submit a separate set of solutions. (Please indicate which other students you collaborated with, if any.) Class participation and discussion will be an important component of your grade.

• Exams: There will be one midterm exam and a cumulative final exam. Either of these exams may be takehome exams.

• Grading Policy: Grades will be computed according to the following percentages:

  Homework	20%
  Project	10%
  Midterm	30%
  Final	40%