MAT 530 Topology, Geometry I, Fall 2012.
- Instructor: Oleg Viro, office 5-110 Math Tower,
- Office hours: Tuesday 1:15pm-2:15pm
and 4pm-5pm in 5-110 Math Tower
or by appointment.
- 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.
- O.Ya.Viro, O.A.Ivanov, N.Yu.Netsvetaev, V.M.Kharlamov, Elementary
Topology: Problem Textbook, AMS, 2008.
The last part of the course is covered in the following text
Topological manifolds (updated on 12/11),
which is organized as a continuation of the main textbook.
Midterm exam will be on October 16 (Tuesday), in class.
It will cover general topology up to product of topological spaces
inclusively. Among the problems there will be theorems with proofs from the
No books or notes are allowed on exams.
Homework: weekly assignments will be posted on
Homework will constitute a significant part of your course grade.
Homework 1 is due on 9/10 (postponed from 9/6).
Homework 2 due on 9/13.
Homework 3 due on 9/20. By Tuesday 9/18 revisit all the definitions in sections 2, 3, 4, 5, 6, 10 and 11. Be prepared for
reproducing any of the definitions in writing.
Homework 4 due on 9/26.
Homework 5 due on 10/4.
Homework 6 due on 10/11. By Tuesday 10/9 revisit
all the definitions in sections 12 - 18. Be prepared for reproducing
any of the definitions in writing.
By Tuesday 10/30 revisit all the definitions and formulations of theorems in sections 21, 22 and 30.
Homework 7 due on 11/1.
On Tuesday 11/13 after the lecture one can make up the midterm exam.
Homework 8 due on 11/15.
Final Exam will be on Monday, December 17, 11:15AM-1:45PM
in room 183 of Earth and Space Sciences Building. Here
is a very detailed program for the exam.
- 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.