Math 430, Topology, Fall 1999

Meetings:
in 143 Atgeld Hall, MWF at 11am (sect D1).
Web address:
Course information is available online at http://www.math.uiuc.edu/~jms/m430
Professor:
John M. Sullivan, jms@uiuc.edu, 326 Illini Hall,
244-5930 (with answering machine); mailbox in 250 Altgeld.
Office hours:
Tentatively, Monday at 2 and Friday at 10. or by appointment.
Prerequisites:
Undergraduate group theory and complex analysis.
Required Texts:
Bredon, Topology and Geometry, GTM 139, Springer
Fulton, Algebraic Topology, GTM 153, Springer
Math 430 covers three areas of algebraic topology:

DeRham cohomology in the plane
Path integrals, winding numbers, deRham cohomology, Mayer-Vietoris, fixed point theorems, Jordan curve theorem. (Fulton, Chap. 1-6,10)
Covering spaces and the fundamental group
Fundamental group, Hurewicz theorem, covering spaces, group actions, deck transformations, classification and existence of covering spaces, van Kampen Theorem. (Fulton, Chap. 11-17)
Singular homology
Eilenberg-Steenrod axioms, homology and fundamental group of spheres and tori, fixed point and separation theorems in higher dimensions. (Bredon, Chap. 4)
Each of these topics makes up about a third of the course. The two midterms will approximately cover the first two topics, respectively, and will be held in early October and early November. The take-home final exam for this course will have questions from each area and questions which combines ideas from different areas.