Math 74/114

Spring 2021

Topology II

General Information









Vladimir Chernov

Contact Information

Office: 304 Kemeny Hall

Telephone: (603) 646 2421



Course Meeting times:

Monday 2:35-3:40 PM Zoom ID 926 9176 6935

Wednesday 2:35-3:40 PM Zoom ID 926 9176 6935

Friday 2:35-3:40 PM Zoom ID 926 9176 6935


(x-hour Thursday 1:40-2:30 PM Zoom ID 926 9176 6935)




Tentative Office Hours:

Monday 4-5:30 PM Zoom ID 983 4122 9775

Tuesday 4-5:30 PM Zoom ID 983 4122 9775

Friday 4-5:30 PM Zoom ID 983 4122 9775

and by appointment. The Zoom password will be sent to the class prior to the first class and is also available from your instructor.



Text Book

Allen Hatcher “Algebraic Topology” First Edition

Course grade will be based on

Homework 50 points

Middle of the Term Presentation and Discussion 100 points

End of the Term Presentation and Discussion 150 points

Total 300 points



Late homework will not be accepted unless it is excused in advance for serious reasons. Unexcused late and missing homework counts zero.



ORC Description: This course provides a foundation in algebraic topology, including both homotopy theory and homology theory. Topics may include: the fundamental group, covering spaces, calculation of the fundamental group, singular homology theory, Eilenberg-Steenrod axioms, Mayer-Vietoris sequence, computations, applications to fixed points and vector fields.


Prerequisites:  Math 31/71 and Math 54 and permission of Instructor or Math 54 and Math 101.


Oral Presentations and Discussions: There will be a middle of the term and end of the term oral presentation and discussion. Each one will cover one of the course topics. They should be done during the periods Monday April 27-  Friday May 1 and Friday June 5 - Sunday June 7, respectively. The list of possible topics will be assigned in the week before the one when the presentations are due. The presentation will be via a personal  Zoom meeting and, in addition to the topics presented, they will involve a general discussion of the other course topics.



Written homework will be assigned after each lecture. The written homework assignment can be found here. All homework  will generally be due by Canvas (preferred) or by email by the class time on Wednesday following the week when it  was assigned, unless announced otherwise.

Late homework will not be accepted unless it is excused in advance for serious reasons. Unexcused late and missing papers count zero.

Honors Code: Collaboration on Homework is permitted and encouraged but NO COPYING. On oral presentations and discussions NO HELP given or received. In general, when in doubt, ask before doing. Please see also the Statement of Community Standards and Accountability that  explains the Academics Honors Principle.


Consent to Recording: (1) Consent to recording of course and group office hours a) I affirm my understanding that this course and any associated group meetings involving students and the instructor, including but not limited to scheduled and ad hoc office hours and other consultations, may be recorded within any digital platform used to offer remote instruction for this course; b) I further affirm that the instructor owns the copyright to their instructional materials, of which these recordings constitute a part, and distribution of any of these recordings in whole or in part without prior written consent of the instructor may be subject to discipline by Dartmouth up to and including expulsion; b) I authorize Dartmouth and anyone acting on behalf of Dartmouth to record my participation and appearance in any medium, and to use my name, likeness, and voice in connection with such recording; and c) I authorize Dartmouth and anyone acting on behalf of Dartmouth to use, reproduce, or distribute such recording without restrictions or limitation for any educational purpose deemed appropriate by Dartmouth and anyone acting on behalf of Dartmouth. (2) Requirement of consent to one-on-one recordings By enrolling in this course, I hereby affirm that I will not under any circumstance make a recording in any medium of any one-on-one meeting with the instructor without obtaining the prior written consent of all those participating, and I understand that if I violate this prohibition, I will be subject to discipline by Dartmouth up to and including expulsion, as well as any other civil or criminal penalties under applicable law.


Disabilities:  Students requesting disability-related accommodations and services for this course are encouraged to schedule a phone/Zoom meeting with me as early in the term as possible. This conversation will help to establish what supports are built into my course. In order for accommodations to be authorized, students are required to consult with Student Accessibility Services (SAS; Getting Started with SAS webpage;; 603-646-9900) and to request an accommodation email be sent to me. We will then work together with SAS if accommodations need to be modified based on the learning environment. If students have questions about whether they are eligible for accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.


Mental Health: The academic environment at Dartmouth is challenging, our terms are intensive, and classes are not the only demanding part of your life. There are a number of resources available to you on campus to support your wellness, including your undergraduate dean ( ) and the Student Wellness Center ).


Student Religious Observances: Some students may wish to take part in religious observances that occur during this academic term. If you have a religious observance that conflicts with your participation in the course, please meet with me before the end of the second week of the term to discuss appropriate accommodations.