Math 70800, Spring 2021, CUNY GC
Monday & Wednesday, 12 - 1:30 pm, online
- This class meets online. Information about the online classroom has been emailed to the students.
- (2/4/21) HW 1, Notes on Classification of surfaces and Quotient Spaces has been posted below.
- (2/24/21) HW 2, Notes on Abelian groups and homomorphisms has been posted below.
- (3/8/21) HW 3 has been posted below.
- (4/10/21) HW 5 has been posted below.
- (4/19/21) Review Sessions (same Zoom link as the class):
(1) Fundamental Group review: Friday 4/23, 3 - 4:30 pm
(2) Covering Spaces review: Thursday 4/29, 4 - 5:30 pm
- (5/5/21) HW 6 has been posted below.
Instructor: Abhijit Champanerkar
Wednesdays 2 - 3:30 pm online (same link as classroom)
Algebraic Topology by Allen Hatcher, Cambridge University
Press, ISBN 0-521-79540.
We will cover Chapters 2, 3 and some
additional topics at the end of each chapter.
Homework & Exam:
- Elements Of Algebraic Topology by Munkres, Westview Press.
- Homology theory. An introduction to algebraic topology
by James Vick, Springer-Verlag GTM.
Homework will be assigned regularly during
the semester and posted here. Instructions about submitting and
grading homework will be provided on each homework. We will have a
final exam at the end of the semester.
The grade for this class will be determined on basis of
submitted homeworks and the final exam.
Outline of classes
Unless otherwise noted, the section numbers and problem numbers
refer to the textbook Algebraic Topology
by Allen Hatcher.
| Feb 1
|| CW complexes and surfaces (Chapter 0)
|| Surfaces   Quotient Spaces   HW 1
|| Mon Feb 15th
| Feb 8
|| Delta complexes and Simplicial Homology (pg 104-108)
| Feb 15
|| Singular homology and Homotopy Invariance (pg 108-113)
|| Note: Monday 2/15 GC closed
| Feb 22
|| Relative Homology (pg 115-118)
|| HW 2
|| Mon March 8th
| Mar 1
|| Excision and Applications (pg 119-128)
| Mar 8
|| Mayer-Vietoris Sequence (pg 149-153) & Equivalance (pg 128-131)
|| HW 3
|| Mon Mar 29th
| Mar 15
||Degree and Cellular Homology (pg 134-141)
| Mar 22
|| Applications (pg 166-176)
|| HW 4
|| Mon April 12th
|| Mar 29
|| No classes
|| Spring Break
| Apr 5
||Universal Coefficient Theorem
|| HW 5
|| May 3rd
| Apr 12
| Apr 19
|| Cup Products
| Apr 26
| May 3
|| HW 6
|| Friday May 28th -->
| May 10
| May 17
|| Note: 5/17 is last day of classes
| May 21
|| Topology Qualifying Exam
|| Friday May 21, 10am - 1pm
About online classes
- Online classroom Information about the online class
will be emailed to students.
- Do not share the class zoom
information with anybody nor post it online. To attend the class
you either have to be registered for the class or need special
permission from me.
- Join 5 minutes ahead of class time
so we can start in a timely manner.
- Join the Zoom link with
- Mute your mic. You can unmute to ask questions.
- Pdf scanning: Students may have to handin homeworks/exams
as pdf scans of their work. Here is a guide to scan your work to pdf.
- CUNY policy about the recording of remote classes:
Students who participate in this class with their camera on or use a profile image are agreeing to have their video or image recorded solely for the purpose of creating a record for students enrolled in the class to refer to, including those enrolled students who are unable to attend live. If you are unwilling to consent to have your profile or video image recorded, be sure to keep your camera off and do not use a profile image. Likewise, students who un-mute during class and participate orally are agreeing to have their voices recorded. If you are not willing to consent to have your voice recorded during class, you will need to keep your mute button activated and communicate exclusively using the "chat" feature, which allows students to type questions and comments live.
- Proctoring of assessments: Students are required to keep
their cameras on during assesments for this class.
- Academic integrity and Digital etiquette: Cheating in any
form will not be tolerated. Please
see CUNY Policy on Academic Integrity. Online
cheating will be dealt with severely. Please be aware of
proper online class behavior. In the online virtual
classroom repeated offenses will result in being barred from
participation in the class.