Elementary Topology, A First Course: Textbook in Problems by
O. Viro, O. Ivanov, N. Netsvetaev, and V. Kharlamov.
Available for download from
A hardcopy can be purchased from the Copy Center (Thayer Hall, 2nd floor).
Secondary textbook: Algebraic Topology by Alan Hatcher,
Cambridge University Press, 2002. Also available from
||215 Silsby Hall
||10:00 – 11:05
||Th 12:00 – 12:50
||402 Bradley Hall
||TuF 6:00 – 7:00pm;
Th 1:00 – 2:00pm
or by appt.
If time permits, we can venture into the following subject as well:
Fundamental Group and Covering Spaces: homotopy; properties of path
multiplication; definition of fundamental group; theorems of path lifting;
universal coverings and calculations of fundamental groups.
Fundamental Group and Mappings: induced homomorphisms and their
applications (winding number, Borsuk-Ulam Theorem); retraction and fixed
points; homotopy equivalence; covering spaces via fundamental groups;
hierarchy of coverings.
Cellular Spaces: examples of cellular spaces; fundamental group of
a cellular space; Seifert-van Kampen Theorem; one-dimensional homology and
Manifolds and Classification of Surfaces: locally Euclidean spaces
and manifolds; isotopy; classification of one-dimensional manifolds;
triangulation and handle decomposition; topological classification of compact
There will be one take-home midterm and the take-home final exam.
They are scheduled as follows:
You will have the whole final examination period to work on the final
take-home exam, though it should not require more than a few hours if
you know the material.
You are expected to work alone on the exams. You may use any printed
matter (or your class notes) of your choice but you may not consult one
another or other humans. The honor principle applies.
||April 27, Wednesday
||May 2, Monday
||June 3, Friday
||June 7, Tuesday
If you have a legitimate conflict with the exams dates and times, please
contact the instructor as soon as possible, do not wait until shortly before
Exams will not be given early to accommodate travel plans.
We will meet on X-hours (almost) every week
to discuss homework problems. Each time a random student will be
chosen to present his/her solutions to selected problems. These presentations
will count towards the final grade. Please note that you can always
decline an opportunity to present your solutions if you feel
uncomfortable about it.
- Homework sets will be assigned for each class but are to be handed in
weekly. Assignments for Wednesday and Friday on
a given week as well as the one for next Monday are to be submitted in class
next Friday. There will also be appropriate
adjustments for holidays. You can check the exact due dates on the Homework Assignments web page.
- Besides usual written assignments, additional practice problems will be
listed for some classes. You are strongly encouraged to solve these problems, but please do not hand in solutions to them. Their sole purpose
is to help you better prepare for the exams.
- Late homeworks will not be accepted.
Unexcused late and missing papers count
- More details are posted on the Homework
Assignments web page.
The course grade will be based upon the scores for the homework (including
presentations), midterm and final exams.
|In-class presentations of homework
- On Exams: No help given or received. You cannot consult any other
human (students and professors included, but not limited to).
- On Homework: Collaboration is permitted and encouraged, but NO COPYING. Discussions of
the general ideas of the class with instructors, tutors, fellow students and
others are desirable. However, each student is expected to complete his or
her assignments individually and independently.
Students with disabilities who will be taking this course and may need
disability-related classroom accommodations are encouraged to
make an appointment
to see their instructor as soon as possible. Also, they should stop by the
in Collis Center to register for support services.