Introduction to Topology

Summer Quarter, 2011

Instructor: Sergei Chmutov

Classes: July 18 --- August 5.
Monday, Tuesday, Wednesday, Thursday, Friday, 1:30 - 2:20 p.m. at CC-326.

Students are welcome to attend my undergraduate research working group "Knots and Graphs" as well:

1. Point-set topology.

      Open, closed sets. Quotient topology. Compactness. Continuity. Homeomorphisms. Manifolds.
      The Jourdan curve theorem.                 Handout 1
2. Surfaces.
      Orientability. Examples. Surfaces with boundary.                 Handout 2

      Chord diagrams as surfaces with boundary. Classification of 2-manifolds. Euler characteristic.                 Handout 3
3. Fundamental group.
      Homotopy. Fundamental group. Examples.

C. Wayne Patty, Foundation of Topology. Jones and Bartlett Publishers, 2009.
W. Massey, A Basic course in algebraic topology. Springer-Verlag, 1991.
J. Scott Carter, How surfaces intersect in space: an introduction to topology. World Scientific, 1995.