# Introduction to Topology

#### Summer Quarter, 2011

**Instructor:** Sergei Chmutov

- Office: MW-746
- Telephone 292-0819
- email: chmutov@math.ohio-state.edu
- http://www.math.ohio-state.edu/~chmutov/10-11/top/int-top.htm
- Office Hours: Tuesday, Thursday, 2:30 - 3:30 p.m.

**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.