Math 6520: Algebraic Topology
Instructor: Mladen Bestvina
Office: JWB 210
Office hours: Fridays at 1 or by appointment
Text: Hatcher: Algebraic Topology
Meets: MWF 10:45-11:35 in JTB 120
Homework: I will assign it approximately biweekly. I
encourage you to work on it in groups, but of course what you write
should be in your own words. Homework is required to be written in
latex.
Exams: There will be a take-home final.
Required statements
The University of Utah values the safety of all campus community
members. To report suspicious activity or to request a courtesy
escort, call campus police at 801-585-COPS (801-585-2677). You will
receive important emergency alerts and safety messages regarding
campus safety via text message. For more information regarding
safety and to view available training resources, including helpful
videos, visit safeu.utah.edu.
Accommodation: The University of Utah seeks to provide equal access
to its programs, services and activities for people with
disabilities. If you will need accommodations in the class,
reasonable prior notice needs to be given to the Center for
Disability Services (CDS), 162 Olpin Union Building, 581- 5020
(V/TDD). CDS will work with you and me to make arrangements for
accommodations. All information in this course can be made available
in alternative format with prior notification to CDS.
Homework 1, due Jan 22. Tex
file
Homework 2, due Feb 7. Tex
file
Homework 3, due Feb 21. Tex file
Homework 4, due March 16. Tex file I'll be out of town March 3-6
and the following week is spring break, so you have more time on
this assignment, but there is also more work.
Homework 5, due March 27: Hatcher section 2.1:
#6,8,12,17,18,20,22,26,27,29.
Homework 6, due April 11: Hatcher section 2.2:
#1,2,3,7,9,10,12,19,23,28,40; "extra credit": #25,29,42
Homework 7, due April 20. Tex file
Take-home final, due May 4. Tex file
Notes from online lessons:
2020-03-16_More_on_Bordism
2020-03-20_Subdivision_and_Excision
2020-03-23_Applications_and_Calculations
2020-03-25_Simplicial_vs_Singular_Homology__Mayer-Vietoris
2020-03-27_Degree_and_Cellular_homology
2020-03-30_Cellular_Homology__Homology_with_Coefficients
2020-04-01_Invariance_of_Domain__Cohomology
2020-04-03_Kronecker_Pairing_Tor_Ext
2020-04-06_Univ_Coeff_Thm__Cup_Product
2020-04-08_Cup_Product_Continued
2020-04-10__Cross_Product_and_Calculations
2020-04-13_Poincare_Duals_Cup_Product_on_Proj_Spaces_Borsuk-Ulam
2020-04-15__Mayer-Vietoris_method__Kunneth_formula
2020-04-17_de_Rham_thm__Poincare_duality
2020-04-20_Poincare_Duality