Math 210, Manifolds III, Spring 2006

• Lectures: MW 10:00am-11:45am, JBE 360

• Instructor: Viktor Ginzburg; office: 353C Baskin Eng.

• Office Hours: Tu 2:00-3:30pm, W 12:00-1:30pm or by appointment

• References:
  • Topology from the Differentiable Viewpoint by John Milnor, Princeton University Press, 1997.
  • Algebraic Topology by Allen Hatcher, Cambridge University Press in 2002. Available on line: http://www.math.cornell.edu/~hatcher/AT/ATpage.html
  • Introduction to Topology by V. A. Vassiliev, AMS 2001.
  • Differential Topology by M. Hirsch, Springer, 1976.

• Tentative Syllabus: This course is a continuation of the first two courses 208 and 209 in the new geometry sequence 208-210 and 211. In the course we will cover, with varying degree of detail, a few topics in differential and algebraic topology. These include
  • Technical preliminaries with applications: tubular neighborhood theorems, the space of smooth maps and approximation by smooth maps, transversality.
  • Fundamental group and covering spaces, the Seifert - van Kampen theorem and examples of calculation of the fundamental group.
  • Degree revisited, intersection number, Euler characteristic, examples and applications.
  • Introduction to (co)homology, the de Rham theorem, homotopy groups.

• Coursework: There will be weekly homework sets and a take-home final.

• Homework Assignments:
  • Homework Assignment I (pdf file): Tubular neighborhoods and approximations of continuous maps by smooth maps, due Monday 4/17-2006
  • Homework Assignment II (pdf file): Transversality, due Wednesday 4/26-2006
  • Homework Assignment III (pdf file): Fundamental group, due Wednesday 05/03-2006
  • Homework Assignment IV (pdf file): Transversality and degree, due Wednesday 05/17-2006
  • Homework Assignment V (pdf file): Euler characteristic, due Wednesday 05/24-2006
  • Final Homework Assignment (pdf file): due Wednesday 05/31-2006