INSTRUCTOR: Sasha Voronov
OFFICE: VinH 324
PHONE: (612) 624-0355
E-MAIL ADDRESS: voronov@umn.edu. You are welcome to use e-mail to send questions to me.
INTERNET: All class announcements and assignments will be posted on the class homepage http://www-users.math.umn.edu/~voronov/8306-21/ and NOT handed out in class.
OFFICE HOURS (tentative): Mon 1:25-2:15, Wed 2:30-3:20, Thu (on Zoom) 2:30-3:20, or by appointment.
TEXT: Algebraic Topology, 1st edition, 2002, by Allen Hatcher. Available for purchase at the bookstore and online, and for free electronically through the library or a direct link to Hatcher's web page. There is also a hard copy on reserve at the Math Library. A list of Errata to the printed edition is posted on Hatcher's text web page.
J. P. May's Concise Course in Algebraic Topology might be a good alternative.
CONTENT: This school year, the course will run as a one-semester course. There will be no continuation in Spring 2022. But you will have options to take Math 8307 later or take 8306-07 entirely, as it will likely be taught differently by a different instructor.
In the Fall semester, we will cover the following topics: singular homology and cohomology with coefficients, the Eilenberg-Steenrod axioms, the universal coefficient theorems, products in homology and cohomology, fiber bundles, fibration and cofibration sequences, homotopy groups, and spectral sequnces. This corresponds to a selection of topics from all the chapters of the textbook.
PREREQUISITES: Math 8301: Manifolds and Topology (1st semester). In reality, it is much less: familiarity with point-set topology, fundamental group/covering spaces and basic homology. However, I will start with a quick review of singular homology, CW-complexes and cellular homology, simplicial complexes and simplicial homology.
GETTING HELP:
GRADING: Based on your homework, which will be due every other week. No exams. Class participation may be taken into account. Grades will be assigned on a curve. I expect you to put enough hard work to earn grades not lower than a B. The curve does not exclude the possibility of everybody getting A's, though, but this happens rather rarely.
COVID-19: :
IMPORTANT DATES:
September 8: First class meeting.
September 20: First homework due.
November 25-26: Thanksgiving Break.
December 15: Last class meeting.
Page created on 09/07/2021; the first homework due date updated on 09/12/21. Office hours updated on 09/20/21.