Math 74/114

Spring 2020

Topology II

General Information









Vladimir Chernov

Contact Information

Office: 304 Kemeny Hall

Telephone: (603) 646 2421



Course Meeting times:

Monday 12:50-1:55 PM Zoom ID 947-670-429

Wednesday 12:50-1:55 PM Zoom ID 549-701-538

Friday 12:50-1:55 PM Zoom ID 478-427-433


(x-hour Tuesday 1:20-2:10 PM Zoom ID 109-606-607)


Tentative Office Hours:

Monday 4-5 PM Zoom ID 932-880-620

Tuesday 4-5 PM Zoom ID 482-887-873

Friday 4-5 PM Zoom ID 167-534-221

and by appointment



Text Book

A.  Hatcher “Algebraic Topology”

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 – Monday June 8, 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 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.

Consent for Video Recording: by enrolling into this course, you consent to video recording of the lectures made by the instructor. See the consent document provided by the dean’s office here


Disabilities: Students with disabilities who may need disability-related academic adjustments and service for this course are encouraged to see me privately as early in the term as possible. Students requiring  disability-related academic adjustments and services must consult the Student Acessibility Service office (Carson Hall, Suite 125, 646-9900). Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on a SAS letterhead to their professor. As a first step, if students have question about whether they qualify to receive academic adjustments and services, 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.