MATE 6540   Topology

Time and place

MJ 9:00--10:15, in M-118.

Topics

We will divide the course into three parts:

Point-set topology: review of topological space, limits and continuity, construction of topological spaces, compactness, limits of functions, numerical functions, connectedness (12 lectures).

Algebraic topology: homotopic paths, fundamental group, induced homomorphism, covering space, index and applications, homotopic maps (6-8 lectures).

Differential topology: smooth manifolds and smooth maps, the theorem of Sard and Brown, the degree modulo 2 of a mapping.

Other topics, as time permits. It is expected that the students will participate in presenting the material (roughly, 2-3 lectures each).

References

"General topology", by Jacques Dixmier, Springer-Verlag, 1984.

"Introduction to Topology", by T.W. Gamelin & R.E. Greene, Dover, 1999.

"Topology from the differentiable viewpoint", by John Milnor, University Press of Virginia, 1965, 1969.

Grading policy

Homework, presentations, exams: 20%+20%+60%.

Homework   updated Apr 26.

Last modified: Mon Apr 26 19:27:22 AST 2010