Office Hours: Tuesday 1-2pm, Thursday 2-3pm by appointment

Office Hours: Mondays from 2-3:30pm, Tuesdays from 3-4pm and by appointment

Prerequisites: Point set topology and abstract algebra, as in Math 120 and 144. Undergraduates require instructor permission to enroll.

Textbook: Allen Hatcher, Algebraic Topology, Cambridge University Press, 2001. Also available online here. We will cover roughly Chapters 0-3 (Chapter 0 as needed).

Tentative Schedule: (which may be adjusted as the quarter goes on)

• Week 1: Basic notions: homotopies (Ch 0); Fundamental group, induced homomorphism (§1.1)
• Week 2: Fundamental group of circle, Brower fixed point, Borsuk Uhlam §1.1); Van Kampen Thm (§1.2)
• Week 3: Van Kampen Thm and CW complexes (§1.2); covering spaces (§1.3)
• Week 4: Covering spaces: action on fibers, universal cover, deck transformations, classification of covering spaces (§1.3)
• Week 5: Simplicial homology; Singular homology, homotopy equivalence; relative homology and excision (§2.1)
• Week 6: Mayer-Vietoris sequences; computation of homology; cellular homology (§2.2)
• Week 7: Axioms of homology (§2.3) Note: NO CLASSES Nov 7 (Democracy Day)
• Week 8: Cohomology Groups (§3.1).
• Week 9: Cup product and the cohomology ring (§3.2)
• Week 10: Topological manifolds; orientation, Poincare duality (§3.3)

Homework Policy: There will be weekly homework assignments given out on Tuesdays, and due the following Tuesday at 11:59PM on Gradescope (unless otherwise noted). No late submissions will be accepted. The lowest homework score will be dropped. You are encouraged to discuss and work together on your homework, but everyone must write up their own solutions. Keep in mind that simply copying solutions from another student or from other sources is a waste of everybody’s time, as well as a violation of the expected standard of academic integrity.

Exams: The current plan is to have an evening midterm exam and a final exam. The exams will be held in person.

Grading: Homework 60%, Midterm 15% and Final 25%.

Important dates:

• Add/Drop Deadline: Friday, October 13, 5:00pm
• Midterm Exam: Thursday, Nov 2nd, 7pm-9pm, room 380D..
• Final Exam: Thursday, December 14, 3:30pm-6:30pm

Students with Documented Disabilities: Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is made. Students should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. For accommodations on exams, please provide the OAE letter no later than one week prior to the exam to allow for adequate time to arrange accommodations.

Academic Integrity: The Honor Code articulates Stanford University's expectations of students and faculty in establishing and maintaining the highest standards in academic work. Examples of conduct that have been regarded as being in violation of the Honor Code (and are most relevant for this course) include copying from another student's work or allowing another student to copy from your own work; plagiarism; revising and resubmitting your work for regrading without the instructor's knowledge and consent; representing as one's own work the work of another. See http://communitystandards.stanford.edu/ for more information on the Honor Code.