INSTRUCTOR: Sasha Voronov
OFFICE: VinH 324
PHONE: 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.math.umn.edu/~voronov/8306/index.html and NOT handed out in class.
OFFICE HOURS: Wed 11-noon, Thu 1:25-2:15 p.m., Fri 1:30-2:25 p.m., and by appointment.
TEXT: Algebraic Topology by Allen Hatcher, 2002. Available in print, on line, and on reserve in the Math Library. If you need another book to consult, I have also put Sato's Algebraic Topology: An Intuitive Approach and Selick's Introduction to Homotopy Theory on two-hour reserve in the Math Library.
GOALS AND PREREQUISITES: The goal of the one-year course is to study the powerful machinery of algebraic topology and provide necessary background for a student planning to work in the fields of algebraic topology, algebraic geometry, algebra, geometric topology, symplectic geometry, K-theory, gauge theory, mathematical physics, etc. The course may be considered an independent course in algebraic topology covering complementary topics to those studied in Math 8301-8302: Manifolds and Topology. However, the full mastery of Math 8301-8302 is not required: you just need to know some basics of homology theory and the fundamental group.
CONTENT: In the Fall semester, we have studied homology and cohomology theories, including the following topics: CW complexes, axiomatic, cellular, and singular homology, the Universal Coefficient Theorem, Künneth theorem, cup products, Poincaré duality. This was covered by Chapters 2 and 3 of the textbook.
In the Spring semester we will study homotopy theory, mostly covered by Chapter 4. This will include homotopy groups, fibrations and cofibrations, exact homotopy sequences, the Whitehead and Hurewicz theorems, Eilenberg-Mac Lane spaces. We will also study a selection of topics, depending on time and interest. These topics may include Postnikov towers, cohomology operations, vector bundles, classifying spaces, characteristic classes, K-theory, cobordisms, etc.
GETTING HELP:
GRADING: Based on your homework and topic presentation. Grades will be assigned on 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 thus happens very rarely.
IMPORTANT DATES:
January 18 - Spring semester classes begin.
March 14-18 - Spring break.
May 6 - Last day of instruction.