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:
http://www.math.osu.edu/~chmutov/wor-gr-su11/wor-gr.htm
TOPICS:
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.
BOOKS:
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.