INSTRUCTOR: Sasha Voronov
OFFICE: VinH 324
PHONE: 624-0355
E-MAIL ADDRESS: voronov@math.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: Tue 2:30-3:30 p.m., Wed 11-noon, Fri 1:30-2:30 p.m., and by appointment.
TEXT: Algebraic Topology by Allen Hatcher, 2002. Available in print and on line.
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, 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 the following topics: CW complexes, homology and cohomology theories (including axioms, cellular homology, the Universal Coefficient Theorem, products in singular cohomology, de Rham cohomology), homotopy theory (including fibrations and cofibrations, homotopy groups). This is all covered by Chapters 2, 3, and 4 of the textbook.
In the Spring semester we will study homotopy theory. This will include exact homotopy sequences, the Whitehead and Hurewicz Theorems, Whitehead products, the James construction, simplicial sets, fiber bundles, classifying spaces, Hopf alegbras, spectral sequences, and K-theory. If time permits, we will do some of the following topics: localization and Bousfield-Kan completion, generalized homology, stable homotopy, cohomology operations, and characteriztic classes.
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.
IMPORTANT DATES:
Monday, January 20 - Martin Luther King, Jr. Day. University holiday.
Wednesday, January 22 - The first course meeting in the Spring.
March 17-21 - Spring Break.
May 9 - Last day of instruction.