Math 430 covers three areas of algebraic topology:
- in 143 Atgeld Hall, MWF at 11am (sect D1).
- Web address:
- Course information is available online at
- John M. Sullivan,
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.
- Undergraduate group theory and complex analysis.
- Required Texts:
- Bredon, Topology and Geometry, GTM 139, Springer
- Fulton, Algebraic Topology, GTM 153, Springer
- 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)