Math 5043 - Algebraic Topology

Spring 2011


instructor	phone #	office	e-mail
Renato Feres	5-6752	Cupples I, 17	feres@math.wustl.edu

Section information: Classes meet on Tuesdays and Thursdays from 1:00PM to 2:30PM, in Lopata Hall 202.

Subject: An introduction to algebraic topology, including the general theory of fundamental groups and covering spaces, homology and cohomology of CW complexes.

Text: The main text is Algebraic Topology by Allen Hatcher. Cambridge University Press, 2002. An electronic version is available online here. Initially, however, I plan to cover the parts of the Math 5041 text concerning de Rham cohomology. That text is: Introduction to smooth manifolds by John M. Lee. (Springer, Graduate texts in mathematics, 2003.)

Tentative list of topics:

review of exterior calculus;
integration of forms, Stokes theorem;
de Rham cohomology, de Rham theorem;
the fundamental group;
van Kampen's theorem;
covering spaces;
simplicial and singular holomogy;
homology computations;
back to cohomology (of CW complexes, if time permits);

Coursework: Grades will be based on weekly homework assignments and a final exam. Assignments are due on the Thursday of each week.

Office hours: tentatively, my office hours will be on Tuesday afternoon, from 3:00PM to 4:30PM and Wednesday from 1:00PM to 2:30PM.

Final and qualifying exam: The final and qual have been set for May 10, from 1:00PM to 4:00PM at Cupples I, 199. The final will be about the material covered during the spring semester, and the qual exam includes the material of both the fall and the spring.