MAT 530 Topology, Geometry I, Fall 2012.
- Instructor: Oleg Viro, office 5-110 Math Tower,
- Grader: Jingchen Niu,
- Class meetings: Tuesday and Thursday, 2:30-3:50pm,
The book is available in the campus bookstore (but can certainly be found for less money elsewhere).
It is the required text. Parts of the homework will be assigned from it,
and there will be required readings.
Homework: weekly assignments will be posted on
Homework will constitute a significant part of your course grade.
- O.Ya.Viro, O.A.Ivanov, N.Yu.Netsvetaev, V.M.Kharlamov, Elementary
Topology: Problem Textbook, AMS, 2008.
- Topological structure in a set
- Metric spaces
- Subspaces of a topological space
- Continuous maps
- Separation axioms
- Countability axioms
- Sequential compactness
- Product of topological spaces
- Quotient topology
- Fundamental group and coverings
- Fundamental group and high homotopy groups
- Dependence of fundamental group on the base point
- Calculations of fundamental group using universal coverings
- Behavior of fundamental group under a continuous map
- Classification of coverings
- Applications of fundamental group
- Topological manifolds
- One-dimensional manifolds
- Triangulated two-dimensional manifolds
Students with Disabilities: If you have a physical,
psychological, medical, or learning disability that may impact on your
ability to carry out assigned course work, you are strongly urged to
contact the staff in the Disabled Student Services (DSS) office: Room
133 in the Humanities Building; 632-6748v/TDD. The DSS office will
review your concerns and determine, with you, what accommodations are
necessary and appropriate. A written DSS recommendation should be
brought to your lecturer who will make a decision on what special
arrangements will be made. All information and documentation of
disability is confidential. Arrangements should be made early in the
semester so that your needs can be accommodated.